Mathematical Operations With Significant Figures

Adding and Subtracting with Significant Figures

When adding or subtracting numbers with significant figures, the result should be rounded to the same decimal place as the least precise number. Let's understand the process through an example.

onsider the following addition:

12.345

+ 0.56

_______

To ensure the correct number of significant figures in the result, we need to determine the least precise number involved in the calculation. In this case, it is 0.56, which has only two decimal places. Therefore, the final result should be rounded to two decimal places. Performing the addition, we get:

12.345

+ 0.56

_______

12.905

Rounding the result to two decimal places, we obtain:

12.905 ≈ 12.91

In this example, the final result has been rounded to the same decimal place as the least precise number (0.56).

When subtracting numbers, the same rule applies. The result should be rounded to the same decimal place as the least precise number. The process is similar to addition but with subtraction operations.

189.30

- 20

_______

179.30

Once again, in this case the value of 20 has the least number of decimal places and is our least precise measurement. Therefore, we must round to the nearest whole number since 20 does not have any decimal places. 

179.30 ≈ 179

We use our standard rounding rules such that the final value is 179. 

It is important to note that rounding should only be performed on the final result and not on intermediate steps during the calculation. Rounding at intermediate steps can introduce errors and lead to incorrect results.

Multiplying & Dividing With Significant Figures

When multiplying or dividing numbers with significant figures, the result should be rounded to the same number of significant figures as the least precise number. Let's explore this concept with an example.

Consider the following multiplication:

2.5 × 3.147

To determine the number of significant figures in the result, we need to identify the least precise number involved in the calculation. In this case, it is 2.5, which has two significant figures. Therefore, the final result should be rounded to two significant figures. Performing the multiplication, we get:

2.5 × 3.147 = 7.8675

Rounding the result to two significant figures, we obtain:

7.8675 ≈ 7.9

In this example, the final result has been rounded to two significant figures, consistent with the least precise number (2.5).

When dividing numbers, the same rule applies. The result should be rounded to the same number of significant figures as the least precise number. The process is similar to multiplication but with division operations.

Similar to addition and subtraction, rounding should only be performed on the final result and not on intermediate steps during the calculation.