Hi everyone, I hope you are doing well. Today in this post we can discuss significant figures. Significant figures can be evolved and traced a few hundred years ago and they can be developed from time to time according to the precise calculations that can be done in mathematics and modern science and technology.
The origin of significant figures can be traced to ancient times in Greece, Egypt, or many other countries where they can be used as Significant figures in calculations or mathematics. With time these significant figures can be used by astronomers, mathematicians, and scientists as well. To measure accurate and precise measurements they can use significant figures with scientific notation. In modern physics and mathematics, significant figures can be used essentially.
Now we can start our detailed discussion about significant figures and their definition, rules, examples, and problems in detail.
Details of significant figures are given below:
Significant figures can be defined as:
"In the number or calculated value the specific digits which provide precision and accuracy and also impart and convey the necessity of digits in the calculated measurement."
Significant figures include the zero or the nonzero digits. Significant figures are also known as significant digits and sig figs. When we make measurements or calculate the measurement such as when we measure length, pressure, and volume and the measured value is large then we can use significant or scientific notation method. or the most capable digits are estimated and called significant figures.
Such as if we measure the volume of a cylinder and the measurement is approximately equal to 3.97L and the uncertainty is approximately equals to 0.04L. The actual volume of this cylinder is approximately between 3.93L and 1.01L, but we can't know the certain digits in this measurement completely. But all of these three figures are called significant figures.
Additionally, the value 345.0 has only 3 significant figures 3,4, and 5 the o digit is not termed as a significant figure because it is only a placeholder.
Some digits are not to be considered as a significant figure. So the types of digits that can't be considered significant figures are given below:
Spurious
Leading zero
Trailing zero
The zero can only be present in the value or measurement as a placeholder. For example 1800 the last two zeros were only a placeholder but we can write the scientific notation we can raise the power of ten but in significant value, we only estimate and choose the figures that can provide accurate and precise measurement.
The zero which can be present at the start of measurement and the value is known as leading zero. For instance, 00367 the first two zeros (00) known as leading zero and it can’t be a significant figure in this value 3,6, and 7 are the significant figures. Another example is 0.00456089 in this value the leading zero is not a significant figure but the zero which is present in between the digits like 6,0,8 and 9 is referred to as a significant figure.
Spurious digits are those when we do calculations on the instruments then the high-resolution measurement results precisions and the accuracy digits are known as spurious digits.
Another example is if the zero is present in the value after the decimal it can be considered a significant figure like 12.00 then these two zeros are also significant figures and in this value, the total no of significant figures is 4 but if the decimal is not present like 12300 then the last two zero is not considered as significant figure and in this value, the total significant digits are 5. After the decimal point, the zero is also considered as the significant figure for example 1.000 the last trailing zeros are also the significant figures and the total significant figures in this value is 4. But if the decimal is not present like 1000 then this value has only one significant figure and trailing zeros are only a placeholder.
Some examples of significant figures are given below:
123790: All digits in this value are known as significant figures.
0.0056:in these digits the leading zero is not a significant figure the last two 5,6 are significant figures.
34986097: all digits are significant figures and the zero which is present inside them like 6,0,9,7 all are significant figures.
1001: all digits are the significant figures.
To identify the significant figures from the measurement and for the value, there are some rules. The rules that can help to identify the significant figures are given below:
Non-zero digits in the measurement are to be significant
Between the two significant digits, the zero is also a significant figure.
Starting, leading zeros are not a significant figure.
Zero after the decimal point on the right side can also be a significant figure.
Trailing zero without the decimal point is not significant.
All non-zero digits in the measurement or the value are significant figures some examples are given below:
9144 all the digits in this value are significant. So the total significant digits is 4.
1.5678 all the digits after decimal or before decimal are considered as significant figures and the total significant digits in it is 5.
568.9 these all digits are significant figures.
The digit zero is not to be considered to be significant but in between the two the significant digit zero also becomes a significant digit some examples are given below:
10054 in this value all digits including zero are referred to as significant figures.
102.60809 these all digits are considered significant figures the zeros after the decimal point are also considered significant figures.
101.101 in this value all digits are also considered as the significant digits or figures.
The starting or the leading zero is not considered to be a significant figure it can only considered as a placeholder some examples are given below:
000102 in this value last 3 digits 1,0and 2 are called significant but the starting three zeros are not considered to be significant but it is only placeholder or leading zeros.
0.065 the last two digits 6 and 5 are sig figs but the starting zero or zero after the decimal point is not considered a significant figure.
The trailing zero, the zero on the right side after the decimal point can considered a significant figure. Some examples are given below:
1.89900 these all digits are considered to be significant digits. In this value, the digits 1,8,9,9,0,0 all are significant figures including the trailing zeros.
0.1200 in this value 4 digits are called significant figure 1,2,0 and 0 are significant figures which are trailing zeros but the first leading zero is not considered as the significant figure.
The trailing zeros without the decimal point are not considered as a significant figure. some examples are given below:
19900 the first 3 digits 1,9 and 9 are considered as the significant digits but the last trailing zeros are not to be considered as the significant figure.
1096800 in this value the first 5 digits are considered to be significant but the last trailing zeros are not a significant digit or a figure.
The rounding-off technique can be used in mathematics in all calculations. In this technique the last digit if it is greater than 5 then it can be added to the previous number. for representing the rounding off number we can use n. To round the significant digit with n there are some rules which are given below:
In the measurement value if the last digit is greater or equal to the 5 then we can +1 inti the previous digit. For instance, 1.345 then after rounding the digit the new value is 1.35 and it has 3 significant figures now.
Another example is if we have 5 significant figures like 5.9867 then after rounding off the last digit the new value is 5.987 and they have only four digits in it.
Now if we have the last digit less than 5 then it can’t be added to the previous number some examples are given below:
1.563 the last digit is less than 5 so it can’t added 1 to the previous digit and the significant figure in this value is 4. Another example is that 67.91 has the 4 significant figures and they can’t be changed because the last digit value can’t be added.
To calculate the numerical value of significant figures for nonzero significant figure x and for the precision and accuracy p we can use the formula which is given below:
10n. Round (x10n)
Where the n is equal to,
n=[log 10(x)]+1-p
In the measurements precision and accuracy, both are essential. Generally, we can use precision for the stability of the measurements with repeated values and the accuracy used for the closeness to the actual and accurate measurement of the thing and the object. but with time in modern technology and science, both precision and accuracy are termed for trueness or the most closeness exact value of the measurements. In the scientific community, the accuracy and precise measurement of the object is essential because without accuracy the measurements and problems become more complicated That is why accuracy and precision both are essential for measurements.
In addition and subtraction, the result of measurements can calculated with the same decimal point before and after the addition and subtraction for example:
12.56+ 0.5=13.1 they have the 3 significant figures in it another example is that
67.9+9 =76.9 and the significant figure in it is 3.
The result that can be taken from measurement and the result after division and multiplication of values both have the same significant figures some examples are given below:
4.56 1.4 = 6.384 and we should rounded to 6.4 then they have 2 significant figures like before the division. another example is that 2.44 then it is equal to 9.6 they have also 2 significant digits like before the multiplication or division.
In the measurement, certainty means that we confidently know the significant digit in the measurements. This known digit conveys and provides the precision of measurement and is also considered reliable because accuracy and precision are very essential in the measurements.
For example, if we can measure the length of an object with a ruler that has a millimeter marking and the measurement is equal to 24.87 then the digits 2,4,8, and 7 are certain because measurement tools can provide precise and accurate measurements.
Rather uncertainty in the significant figures means that which measurements we can take are not precise and accurate and we have doubts about them. When an unskilled person or limited measurement tool is used for measurement then chances of uncertainty increase because a skilled person can take accurate and precise measurements of the object and the high precision measurement tool is also needed.
For example, if we can measure the length and the measurement is 24.56 then the last digit 6 creates uncertainty because it can be rounded off and the original length can't be measured precisely and efficiently. So that's if we want to remove uncertainty then we again measure the length and then determine the significant figures in it.
Some examples of significant figures are given below:
406.62 all digits in this are significant figures and the total significant figures is 5.
0.00034 the last two digits are signification figures and the starting zeros are leading zeros.
12090 all are significant figures and the last zero is only a placeholder.
74.0 the zero after decimal is also a significant figure the total significant figure is 3.
67.08 in this all digits are significant figures and the total is 4.
These are some common examples of significant figures.
Some practical problems to understand the significant figures are given below:
Identify the significant figures in the given problems:
7696
0.0074
690.00
60.09
74.0
Solutions to these problems are given below:
All 4 digits are significant figures.
Leading zeros are not significant digits but the last 2 digits 7 and 4 are significant.
All 5 digits including zero after decimal are also considered significant digits.
6,0,0 and 9 all digits are considered significant figures.
7 and 4 including trailing zero after the decimal are also considered significant figures.
The calculation to determine or calculate the significant figures some problems are given below:
26.7+ 8.1
62.4 0.04
2.4+ 9.2
58.0+ 4.5
0.056/0.0007
The solution to these problems is given below:
34.8 in this value 3, 4, and 8 are significant figures.
2.496 in this value 4 significant digits are present.
11.6 in this solution all digits are considered significant figures.
62.5 in this solution of a problem all digits are significant digits.
80 are the solution and both are significant figures.
To determine the significant figures, perform the following operations:
(2.7+ 4) 7.9
(5.6 8.9) + 8
Solutions to these problems are given below:
(6.7) x 7.9
=52.93 In this solution, all 4 digits are significant figures.
(49.84) + 8
= 57.84 In this solution, all 4 digits are significant figures.
Hi friends, I hope you all are well. In this post, we will talk about scientific notation. Scientific notation is an essential tool that scientists and engineers can use. Archemdies presented the idea of scientific notation in the 3rd century BC. His work and scientific notation ideas are based on the novel of time, known as place value.
Scientific notation ideas have evolved over many centuries but are finally represented by Archimedes. In the 16th or 17th century, mathematicians continued to adopt changes in them and invent many other new notable contributions like Rene Descartes who developed algebraic notation. Scientific notation is a way in which we can express large number values in short form in the form of an exponent or a decimal form.
Scientific notation not only simplifies the equation, but it can also help scientists and engineers to do calculations easily. In the United Kingdom scientific notation is also known as standard form or standard index form. Scientific notation is commonly used by scientists and on scientific calculators it is referred to as “SCI” display mode.
Scientific notation in detail is given below:
Scientific notation is defined as:
"it is the simplest way to express the large number into the small number or into in decimal form."
It can used by scientists, mathematicians, and or engineers to simplify the calculation and express the calculation in a very efficient way. In scientific notation, the number is expressed in the product form and they have two factors.
Generally, the scientific notation is written in:
N=m 10n
There:
Some examples of scientific notation are given below:
Covert 89,700 to scientific notation.
Firstly move the decimal to get 8.79
The decimal moved 3 places to the left, then the exponent is 8.
Then the scientific notation is 8.79103
Convert 0.0000023 into scientific notation:
Firstly move the decimal to get 2.3.
The decimal moved 6 places, then the exponent is 2.
Then the scientific notation is 2.3106.
We can write any real number equation in the form of m10n in various ways. In the normalized scientific notation, the value of m is 1 or greater than 1 but it is always less than 10 and the value of n depends upon the larger value or decimal place. thus equation 550 can be written as 5.50102. this scientific notation helps to compare the number easily in an efficient way if the exponent value is large that means that the number is normalized as compared to smaller exponents. The order of magnitude can be assumed when we subtract the exponent by separating the numbers.in the table of logarithms, we can use this form of numbers to solve the log questions. The exponent in the normalized equation is negative if the value ranges between 0 and 1 for example: 00.6 then it can be written in 610-2. the exponents may be equal to 10 if the real number value is large like 0.0000000009 then it can be written as 910-10.
In many fields, typically or generally normalized equation is used to express large numbers of values into simple and efficient decimal form. Exponential notation is also referred to as normalized notation. But in different fields, unnormalized or simple notation or equations can be used. Generally, the latter term of notation is more used where the value of m is not suppressed in the range between 1 to 10 and the base of the exponent may be changed or other than the 10.
Generally, calculators or computer programs use small or large number values to present scientific notation or in some calculators, all the numbers are present or configured uniformly.
The capital letter “E” or the small letter “e: can be used to represent or express the exponent which means “ten raised to the power of”. Typically in all computers or programs scientific notation or normalized notation can be abberived or represented in different styles. But the equation men is the scientific notation like m is the coefficient and the e is base 10 or n is for the exponent and it can be written as men or m10n. For example, 1.000 can be written as 1103 or also written as 1e3.
On the scientific calculator, the engineering notation can be written or expressed as “ENG”. The engineering notation is different from normalized notation because the value of exponent n is suppressed in normalized notation. Thus the value of m ranges in 1 ≤ |m| < 1000, other than 1 ≤ |m| < 10. So that's why sometimes the engineering notation is also known as scientific notation.
In engineering notation, the exponent value can be orally read by using prefixes such as nano, pico, Giga, and others. For example, 14.510-9 can as read as fourteen-point-five nanometers and can also be written as 14.5nm.
The number of digits in the value is used to find the degree of accuracy and precision in a value.
Significant figures include all nonzeros or zero digits but the first and the last zero digits are not significant figures if zero is present in between the numbers like 1,2,3,4,5 and so on then it is also called a significant figure. Some examples are given below:
456709800 In this value 7 significant figures are present and at the last two zero is only a placeholder and not referred to as significant figures.
Then 008809 in these values there are 4 significant figures present and the starting first two zeros are not called significant figures.
So when we convert 123459900 values into normalized or scientific notation then all significant figures are present and the nonsignificant figure is removed as 123459900 has 7 significant figures then it can be written in scientific notation as 1.234599108 or also written as 1.23459900108. thus the advantage of scientific notation is to signify the significant figures efficiently.
In scientific measurement, it is essential to record or measure all known digits from the measurement which can be calculated, and then estimate one or more digits if any information about this digit is acquirable. The estimated digits provided more information and became a significant figure because the estimated digits can provide more accurate and precise information about the leading and the ending digits.
The information that we can take from the estimated digit can help in the notation. This information also helps to choose the final digits or digits that are present in the value. For example, the estimated mass of a proton can be equal to 1.67262192369(51)10-27 kg. But in this value, the error occurs when we estimate the digit inefficiently and can be written as 5.110-37 and this estimated digit can increase the standard error or some other possible errors.
The rules that are used to convert the number into scientific notation are given below:
Identify the coefficient
Determine the exponent
Base
Non-zero integer
Positive or negative integer
Add or subtract the coefficient
Arithmetic operation with scientific notation
When we move the decimal point in the value then the original number which becomes the coefficient a is taken like 230000 then the decimal moves in it and becomes 2.3 and the 2 becomes the coefficient in the scientific notation.
Count the number of decimals that we moved in the value and this count becomes the exponent. For example: We have a value of 46000
Then it becomes, 4.6
The total no of decimals that we moved in the value is 4 then the exponent is 4 the value becomes 4.6x104.
The base of the exponent in the scientific notation is always 10.
The exponent is always a value it is always a non-zero integer like 104 or 108.
When we move the decimal from right to left then the exponent integer is positive. Example:
46000 then 4.610+4
When we move from left to right then the exponent integer is negative. Example
0.00677 then 6.7710-3
If the exponent is the same then we simply add or subtract them. Because the same exponent can be added or subtracted and also we can multiply or divide with them. For example:
3.4106 + 9.7106
The exponent is the same then we add them and then rewrite
3.4+9.7=10.04
Then rewrite them into scientific notation
10.04106 then the new scientific notation is
1.004107
In the division method, we divide the coefficient and subtract the exponent. An example is given below:
81062104= 8106-42
=4102
To add or subtract the scientific notation, the same exponent must be necessary. And adjust the equation if needed. An example is given below:
= 2.6103+ 4.0104
Then firstly we adjust the equation to same the exponent of both equations,
2.6103= 0.26104
Then add or subtract them,
=0.26104+ 4.0104
=4.26104
When we multiply the scientific notation then we add the exponent and multiply the coefficient.
Such as,
=(2104) (6102)
Then,
= (26) 104+2
So,
= 12108
Real-world applications of scientific notation in different fields are given below:
Chemists use scientific notation to measure or calculate the atomic size or the atomic level. Such as Avagardo’s number which can be written scientific notation 6.0221023 which can be approximately equal to the one mole in an atom or a molecule.
In space, astronomers used scientific notation to calculate the vast distance. Because in space the distance between the moon, the sun, and other planets is vast so that's why to calculate this distance in a short or efficient way astronomers used scientific notation. For example, the distance between the Earth and the nearest star is approximately equal to 4.241013 kilometers.
Engineers work on a large scale and calculate the calculation in a very precise and efficient way so that is why they use scientific notation to express large number calculations in short form. For example, the circumference of the earth which can calculated by engineers is 4.007107.
In physics, scientists can deal with very large and small quantities of measurements so that’s why to write these measurements in an efficient way they can use the scientific notation method. For example, the speed of light is 3.00108.
To become a scientist or for a scientific education understanding the scientific notation is essential. Scientific notation education starts in middle school but is explained in detail at higher levels. To become a scientist and, if we choose the engineering and technology career then the education of scientific notation is compulsory. because it helps them to calculate or, measure the very large or small measurements in a very precise or accurate form.
With the advantages and utility of scientific notation, it also becomes difficult or challenging for beginners. The common misconceptions that can be faced by beginners are given below:
Arithmetic operations rules can't be understood or can't be used precisely.
Zero can be confused with exponent.
The decimal point can't be placed properly.
Rules which are used for scientific notation can be misunderstood.
Strategies that can be used to manage or overcome these misconceptions or challenges include:
Understand the rules of scientific notation step by step and follow instructions.
Try to solve numerous examples without help.
Understand the rules and solve the arithmetic operations.
With the development of modern science and technology, the use of scientific notation is also increased and it can also be improved from time to time. In modern science and technology, very large and small measurements can be calculated so that’s why the scientific notation method is used to express calculation effectively and accurately because scientific notation also helps to overcome or analyze errors in calculations.
Examples of scientific notation are given below:
The mass of the electron is approximately equal to 0.000000000000000000000000000000910938356 kg
But we can write in scientific notation as,
= 9.10938356×10−31
The circumference of the earth is approximately equal to 40000000m
Then we can write in scientific notation as
= 4107
The distance between the sun and earth is approximately equal to 149,600,000 kilometers
In scientific notation, it can written as:
=1.496108
The mass of hydrogen is approximately equal to 0.00000000000000000000000167kg
In scientific notation, it can be written as,
=1.6710-27
The value 564300 can be converted into scientific notation and written as
=5.643105
Some problems are given below:
Convert the following problems into scientific notation:
456800
0.005544
98076
5544320
0.00000000009
9888800000
Solutions to these problems are given below:
4.568105
5.54410-3
9.8076104
5.544320106
910-11
9.8888109
Multiplication problems are given below:
(2108 ) (4104)
(2.0104) (2102)
Solutions to these problems are given below:
(24) 108+4
=81012
(2.02) 104+2
=4.0106
Division problems are given below:
5.61097.0103
8.41052.0102
A solution to these problems is given below:
8.0105
4.2103
Perform the following operations with numbers in scientific notation:
(5.0104)+(2.5104)
(6103) + (4.0103)
A solution to these problems is given below:
7.5104
6103
Hello friends, I hope you are all good. In our previous lecture, we discussed the SI Base Units in detail and today, we are going to discuss the units derived from these base units. In 1960, the International Committee conference was held and they presented the measurement units that are used to measure all quantities worldwide.SI units are used to make accurate and precise measurements.
SI units are the set of seven basic units called base units and all other units are derived from these base units and called derived units. A set of seven base units is used to measure the physical quantities but derived units are used to measure the complex quantities other than physical quantities. SI units play an essential role in modern technology and sciences.
The basic SI units from which the other units are derived are given below:
Units |
Symbol |
Measure |
meter |
m |
length |
Kelvin |
k |
Thermodynamic temperature |
Ampere |
A |
Electric current |
Second |
s |
Time |
candela |
cd |
Luminous intensity |
Kilogram |
kg |
mass |
mole |
mol |
Amount of a substance |
These units are the building blocks of all others known as derived units. Derived units are the combination of these base units in the form of an algebraic combination.
SI-derived units which are also known as coherent-derived units are derived from base units which can be expressed in ratio, product, or exponential form. Some derived units have dimensions but some do not because their demission cancels through their ratio or product.
Derived units are used to measure the complex quantity. Derived and coherent derived units have specific names, symbols, units, and dimensions. All derived units have dimensions except steradian or radian. 22 derived units, their names, symbols, and dimensions are given below:
Derived quantity |
Specific name |
symbol |
Specific symbol |
SI base units |
Other equivalent units |
Magnetic induction, magnetic flux density |
tesla |
T |
Jm |
Wb/m2 |
kg⋅s−2⋅A−1 |
Plane angle |
Radian |
α,𝛃,ℽ |
rad |
m/m |
— |
Solid angle |
Steradian |
Ω |
sr |
m2/m2 |
— |
Catalytic activity |
Katal |
ζ |
kat |
mol/s |
mols-1 |
Illuminance |
lux |
Ev |
lx |
lm/m2 |
lm.m-2 |
Absorbed dose |
Gray |
D |
Gy |
J/kg |
m2⋅s−2 |
Inductance |
henry |
L |
H |
Wb/A |
kg⋅m2⋅s−2⋅A−2 |
Pressure, stress |
pascal |
р |
Pa |
N/m2 |
kg⋅m−1⋅s−2 |
Electric resistance |
ohm |
R |
Ω |
V/A |
kg⋅m2⋅s−3⋅A−2 |
Celcius temperature |
Degree Celcius |
t,δ |
℃ |
k |
k |
force, weight |
Newton |
F |
N |
Kg m/s2 |
kg⋅m⋅s−2 |
Frequency |
hertz |
f,v |
Hz |
1/s |
s-1 |
Energy, work, heat |
Joule |
E |
J |
N/m , w/s |
kg⋅m2⋅s−2 |
Dose equivalent |
sievert |
H |
Sv |
J/kg |
m2⋅s−2 |
Luminous flux |
lumen |
Փv |
lm |
cd/sr |
cd |
Activity of radionucleotide |
becquerel |
A |
Bq |
1/s |
s−1 |
Magnetic flux |
weber |
Փ |
Wb |
V/s |
Vs−1 |
Capacitance |
farad |
C |
F |
C/V |
kg−1⋅m−2⋅s4⋅A2 |
Electric charge |
Coulomb |
Q,q |
C |
s/a |
s.a |
Electric potential difference |
Volt |
Vab |
V |
W/A |
kg⋅m2⋅s−3⋅A−1 |
Electric conductance |
Siemens |
B |
S |
A/V |
kg−1⋅m−2⋅s3⋅A2 |
SI units are used in different fields in chemistry, kinematics, thermodynamics, photometry, kinematics, electromagnetism, or in mechanics. The details are given below:
Derived quantity |
Name |
Symbol |
SI units |
Luminance energy |
Lumen second |
lm.s |
s.cd |
Luminance |
Candela per square meter |
cd/m2 |
m−2⋅cd |
Luminous exposure |
Lux second |
lx.s |
m−2⋅s⋅cd |
Luminous efficacy |
Lumen per watt |
lm/w |
m−2⋅kg−1⋅s3⋅cd |
Derived quantities |
Symbol |
Name |
Electric charge |
C |
Coulomb |
power |
W |
watt |
frequency |
Hz |
hertz |
Force |
N |
newton |
Voltage |
V |
volt |
area |
m2 |
Square meter |
Pressure |
Pa |
pascal |
Volume |
m3 |
Meter cube |
Energy |
J |
joule |
Derived quantities |
Names |
Symbol |
speed |
Meter per second |
m.s-1 |
Jounce |
Meter per fourth second |
m.s-4 |
Angular acceleration |
Radian per second square |
rad.s-2 |
Volumetric flow |
Cubic meter per second |
m3.s |
jolt |
Meter per cubic second |
m.s-3 |
acceleration |
Meter per second square |
m.s-2 |
snap |
Meter per fourth second |
m.s-4 |
Angular velocity |
Radian per second |
rad.s-1 |
Frequency drift |
Hertz per second |
hz.s-1 |
Derived quantities |
Names |
Symbols |
Thermal expansion |
Per kelvin |
k-1 |
Specific entropy |
Joule per kg per kelvin |
J.kg-1.k-1 |
Thermal resistance |
Kelvin per watt |
k.w-1 |
Heat capacity |
Jolue per kelvin |
J.k-1 |
Temperature gradient |
Kelvin per meter |
k.m-1 |
Thermal resistance |
Kelvin per watt |
k. w-1 |
Derived units play a very vital role in physics and many other fields for accurate and precise measurement and also help to understand the physical phenomena. The building blocks of SI units are seven basic units by combining them the all other units derived. Derived units play an essential role in modern science and technology to measure stable and precise measurements.
The importance of derived units in physics is given below:
Standardization and consistency
Efficiency in scientific computation
Practical applications
Simplification of complex quantities
Enhanced power solving
Facilitation of understanding and communication
Interdisciplinary relevance
Details of the importance of derived units are given below:
The use of derived units enhances computational efficacy in physics. Calculations involving derived units are often more straightforward than those using only base units. For instance, the
Unit watt for power simplifies calculation ]s involving energy and time, eliminating the need for repeated conversions from base units. This efficacy is particularly important in complex calculations, simulations, and models, where reducing the number of steps can significantly impact the accuracy and speed of results.
Derived units are not confined to physics alone but are used across various scientific disciplines, fostering interdisciplinary research and applications. For instance, the coulomb, a unit of electric charge, is crucial in both physics and chemistry. The use of common derived units across different fields facilitates collaboration and integration of knowledge, leading to achievements in areas such as materials science, biophysics, and environmental science. This interdisciplinary relevance underscores the versatility and universality of derived units in scientific inquiry.
One of the foremost reasons derived units are vital in their role in standardizing measurement globally. The SI system, established and maintained by the International Bureau of weights and Measures (BIPM), ensures that measurements are consistent and universally accepted. Derived units such as newton(N) for force, the joule (J )for energy, and the watt(W) for power, are constructed from base units like the kilogram(kg), meter(m), and second(s). This standardization is crucial for scientific communication, allowing researchers from different countries and disciplines to compare results and collaborate effectively on confusion or the need for conversion factors.
In practical and industrial contexts, derived units are designed to be more user-friendly for real-world measurements. For example, the hertz(Hz) is used to measure frequency, providing a more practical and comprehensible unit than cycles per second. Similarly. The use of derived units like the lumen(lm) for luminous flix or the sievert (Sv) for radiations enables more precise and accessible measurement and regulation in various industries, including healthcare, engineering, and environmental monitoring.
Derived units provide a clearer and more intuitive understanding of physical phenomena. For example, energy is measured in joules, which convey specific physical meaning, more straightforwardly than its base unit equivalent. This clarity extends to educational settings, where students can grasp complex concepts more easily when they are expressed in familiar derived units. additionally, using standardized derived units in scientific literature and presentations ensures that findings are communicated effectively, fostering a shared understanding among researchers.
Many physical quantities are inherently complex and can't be conveniently expressed using only base units. Derived units simplify these expressions, making them more manageable and intuitive. For instance, pressure is commonly expressed in pascals(Pa) rather than its base unit form of kg/ms-2. This simplification is not merely a matter of convenience but also aids in understanding and interpreting physical concepts more readily. It allows scientists and engineers to work more efficiently, reducing the potential for error and misinterpretation.
Derived units play a crucial role in problem-solving by aiding in dimensional analysis, which involves checking the consistency of equations. Dimensional analysis ensures that equations are dimensionally consistent, meaning that both sides of an equation have the same units. This technique is fundamental in verifying the correctness of quotations, deriving new relationships, and identifying potential errors. For example, ensuring that the units on both sides of Newton’s second law (F=ma) match confirms that the equation is dimensionally consistent and physically meaningful.
Some applications of derived units are given below:
This unit are used for heat, energy, and work. Their application in physics is given below:
Mechanics: the work which is done by a person or an object can be measured in joules. This concept is also used to understand the potential and the kinetic energy.
Thermodynamics: according to the first law of thermodynamics the energy that can be expressed in joules can't be created or can’t be destroyed and the energy in the form of heat can always be measured in joules.
Electricity: in the electrical system the energy which can be used in the form of electricity can be measured in joules because work is also done in it.
These units are used for power, their application in physics are given below:
Mechanical systems: the power that can be consumed in engines or different mechanical systems can be measured in watts.
Electrical engineering: in our daily life or households like bulbs, ovens, and other electronic devices, the electric energy that can be consumed is measured in watts.
Thermodynamics: In cars engines, and other electronic devices which consume electrical energy can be measured in watts.
These units are used to measure electric potential, and their application in physics is given below:
Power distribution: the voltages that can be distributed to the power line can be measured in volts.
Electronics: the electrical devices like capacitors, diodes, and others that can distribute the voltages. These voltages which can be distributed are measured in volts.
Electric circuits: in electric circuits, the potential that can be distributed is measured in volts.
These units are used to measure the magnetic flux density, their applications in physics are given below:
Physics research: In physics research when high magnetic fields are used then these field strengths can be measured in teslas.
Electromagnetism: the magnetic field strength in the magnets can be measured through teslas.
Medical imaging: In the medical field medical devices like MRI machines have also a strong magnetic field which can also be measured in teslas.
This unit is used to measure electric resistance, their applications in physics are given below:
Thermistor: temperature-sensitive resistors use temperature and resistance both and to measure or control the temperature ohm is used.
Circuit design: in electrical circuits where electric current is passed resistance is also present to measure the resistance we can use ohm.
Material science: to manufacture the electronic device, an ohm is used to measure the resistance.
This unit is used to measure inductance, their applications in physics are given below:
Radiofrequency: In radio when the tune is played then the frequencies are matched because during their manufacturing frequencies are measured in hertz.
Electrical engineering: To make inductors and coils of inductance to make a strong magnetic field Henry is used to measure the inductance.
Power supply: to supply the power current smoothly without changing in current and voltage inductors are used.
This unit is used to measure capacitance, their applications in physics are given below:
Energy storage: capacitors which are used in electrical devices are used to store energy and the farad is used to measure the capacitance of a capacitor.
Communication systems: In television, radios, and other electronic devices capacitors are used to store energy.
This unit is used to measure force, their applications in physics are given below:
Aerospace: Newton is used to find or determine the thrust and friction that are produced by engines during flight.
Classic mechanics: Newton is used to determine the forces that are produced by an object or a person. Newton also presented 3 laws.
Engineering: the engineers who build the buildings and bridges calculate the forces to ensure that these can bear stress or not.
This unit is used to measure pressure, applications of Pascal are given below:
Engineering: The engineer used Pascal to calculate the stresses of the material and then used the material.
Fluid dynamics: Blood pressure, atmospheric pressure, and all fluid pressure can be measured and calculated through Pascal.
Meteorology: to measure the climate and weather Pascal is used.
This unit is used to measure electrical charge, their application in physics are given below:
Capacitors: capacitors are used in electrical devices to store energy and to maintain the current flow.
Electrostatics: in the electrostatic experiments coulomb are used to measure the electric charge that flows through them.
Batteries: in batteries, the charge stored that is used after completing the charging.
Derived units are used in various fields to measure complex quantities and physical phenomena that can't be measured by using the base quantities. Derived units like joule, watt, kelvin, coulomb, Pascal, and all others are derived from basic seven base units in the form of exponent. Now derived units are used in modern technology and sciences. Scientists used these units to measure the different quantities precisely and accurately. From time to time, the SI system can also continue to adopt the changes and present more suitable and precise units for the measurement of the quantities. The SI system adopts many changes in its units and redefines them.