Significant Figures: Rules and Their Algebra with Examples and Videos

In physics, measurements are a way of communicating with the Cosmos. Each measurement yields a numeric value. Each digit of a given number is critical to the process of measurement. As a result, some digits are more important or “significant” than others. Let us learn more about these significant figures.

Significant Figures

Your date of birth has three parts: the day, the month and the year you were born in. Suppose I ask you your age in years, which part of your birthdate is is sufficient to answer my question? The least information I need to guess your age is the year of your birth. Therefore, if you tell me the month I can make a more accurate guess of your age and so on.

As a result, we say that each part or each figure improves or decreases the accuracy of a measurement. As a result, we see that each part of the reported number has a definite importance. Thus we say that Significant figures or s.f. are the important digits or digits that improve the accuracy of our measurement. We can identify the number of s.f. in a measured value with the help of some simple rules. Let learn about them.

Significant Figures

Rules To Count The Significant Figures

You can count the number of Significant figures from these rules:

All the reported non-zero numbers in a measurement are significant. For example, 22.13 has 4 and 299792458 has 9 significant digits.
Zeroes sandwiched anywhere between the non-zero digits are significant. For example, 299007900002400000058 has 21 significant digits, 102.4 has 4 and 1.024 also has 4.
Zeroes to the left of a first non-zero digit are not significant. For example, 007 has 1 significant figure and 0.0000102 has 3.
The trailing zeroes or the zeroes to the right of the last non-zero digit are significant if the number has a decimal point otherwise they are insignificant. For example, 0.00001020 has 4 and 70000000000000 has 1 significant figure only.

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Significant figures in the number ’10’!

How many significant figures are there in 10? We just laid down the rules and according to them, ’10’ must have two significant figures. Well, there is something more you need to know. The trailing zeroes in a number without a decimal may or may not be significant.

For example, in the scientific notation we can write 10 as 1 × 10¹. Since only the non-exponent part is used to count the significant figures. So using our rules, we see that 1 × 10¹ has only one significant digit. Similarly, 10 can also be written as 1.0 × 10¹which has two significant digits.

Furthermore, we say that the number of significant figures depends on the precision of the instrument. Usually greater precision means a greater number of significant digits.

Algebra Of Significant Figures

While performing algebraic operations of measured values, we make sure that the result is not more precise than the least precise value reported. Hence the number of significant figures in the result of our calculation should be equal to the number of significant figures in the least precise value.

Addition And Subtraction

The result should have the same number of significant figures, after rounding off as the reading which has the least number of significant digits.

Example: 7.9391 + 6.263 + 11.1 = 25.3021

Since the least precise value is 11.1 which has 3 significant digits so the answer will be rounded such that it also has 3 significant digits. i.e. 25.3.

Multiplication And Division

Example: 12.50×169.1 = 2113.75

Each digit is having 4 significant digits. Therefore, the final answer is rounded off such that it has only 4 significant digits in it i.e. 2114 will be the answer.

Solved Examples For You

The number of significant figures for a force is four when dyne is the unit. If it is expressed in Newton, the number of significant figures will become: (Given: $10^{5} d y n e = 1 N$ )

a) 9 b) 5

c) 1 d) 4

Solution: d) 4. To change dyne into Newton, we need to multiply it with a constant 10^-5. Since the number of significant digits is not changed upon multiplication by an exponential constant, we see that significant digits will remain the same i.e. 4.

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