Question

What is the answer to the following problem, reported to the correct number of significant figures? (9.072 − 8.7497)/ (21.75 ∗ 0.09764)

Answer 1

We have the following operation:

(9.072 − 8.7497) / (21.75*0.09764)

Let's first analyze each single number and determine how many significant figures it has:

>9.072 has 4 significant digits

>8.7497 has 5 significant digits

>21.75 has 4 significant digits

>0.09764 has 4 significant digits (zeroes to the left are not significant figures if they are not precceded by a significant digit from 1 to 9).

So, we can idenfity the operation to be a division (it contains a substraction in the numerator and a multiplication in the denominator, but the division will be the last operation you do before you get the result, so it will determine the number of significant figures, and the number of significant figures of a division is the number of significant figures of the least precise measurement, in this case 4).

So, without further ado:

(9.072 − 8.7497) / (21.75*0.09764) = 0.151765575

The result with 4 significant digits will be 0.1518 (we rounded up the 0.15176 to 0.1518 to get 4 significant digits, using the proper rules for rounding numbers).