Question

Asked Jan 30, 2020

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How many significant figures should be retained in the result of the following calculation?

12.00000 × 0.9893 + 13.00335 × 0.0107

12.00000 × 0.9893 + 13.00335 × 0.0107

Step 1

In multiplication or division involving significant figures, the final answer should be reported as having the same number of significant figures as the number with least number of significant figures in the problem.

For example: multiplication of 2.814 and 2.54 with significant figures.

2.814 × 2.54 = 7.14756

Here, 2.814 has 4 significant figures and 2.54 has 3 significant figures, so the final answer should be rounded off to 3 significant figures, that is, 7.15

Hence, the final answer for the multiplication of 2.814 and 2.54 involving significant figures will be 7.15

Step 2

In addition or subtraction involving significant figures, first we do the simple addition and subtraction of the figures. Then, we need to find out the figure having least number of digits after decimal point. The final answer will be containing the same least number of digits after decimal point.

For example: addition of 1.26 and 102.3 with significant figures.

Firstly, we do the simple addition of the two numbers.

1.26 + 102.3 = 103.56

Now, 1.26 has 3 significant figures but 2 digits after decimal point and 102.3 has 4 significant figures but 1 digit after decimal point. So, the least number of digits after decimal point is 1. So, our final answer should also contain only 1 digit after decimal point. After rounding 103.56 to have one digit after decimal point will give 103.6

Hence, the final answer for the addition of 1.26 and 102.3 involving significant figures will be 103.6

Step 3

Given equation is : (12.00000 × 0.9893) + (13.00335 × 0.0107)

Firstly, doing the multiplication parts as :

(12.00000 × 0.9893) = 11.8716

Here, 12.00000 has 7 significant figures and 0.9893 has 4 significant figures, so the final answer, that is, 11.8716 should be rounded off to 4 significant figures to give 11.87

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