Explain how the uncertainty associated with a measurement is conveyed through the proper use of significant figures.

Significant figures of a number are the digits that are meaningful during the calculations.

i.e. They are the digits that helps in the uncertainty of how many digits are there in the final answer during the calculations.

We know that all the non-zero numbers are significant and the first non-zero digit on the left is known as the most significant figure and the last digit is known as the least significant figure.

Now, we see,

1. Use of significant figures in addition and subtraction.

The rule for the uncertainty is that 'the number of digits after the decimal in the result is equal to the least number of digits after the decimal in each term'.

for e.g.

A. 3.126 + 8.64 = 11.766.

But, according to the rule, we round of the digits after the decimal places to hundredth place as the least number of digits after decimal is 2.

So, 3.126 + 8.64 = 11.77

B. 29.4165 - 234.65 = -205.2335

But, according to the rule, we round of the digits after the decimal places to hundredth place as the least number of digits after decimal is 2.

So, 29.4165 - 234.65 = -205.23

2. Use of significant figures in multiplication and division.

The rule for the uncertainty is that 'the number of significant digits in the result is equal to the least number of significant figures in each term'.

for e.g.

A. 13.1 × 2.25 = 29.475

But, according to the rule, we round of the digits so we have the same number of significant figures as the least significant figures in both i.e. 3

So, 13.1 × 2.25 = 29.5

B. 3.68 ÷ 0.07925 = 46.43533123

But, according to the rule, we round of the digits so we have the same number of significant figures as the least significant figures in both i.e. 3

So, 3.68 ÷ 0.07925 = 46.4

Hence, in this way significant figures helps in the uncertainty during calculations or measurements.