Mohammad learned that the number of significant figures for a given measurement is determined by the inherent uncertainty of the measuring device.

Question

Carry out the following mathematical operations, and give each result to the correct number of significant figures. 

a) 5.18 x 0.0208

b) 21 + 13.8 + 130.36

Answer 1

a) 0.108 In multiplication or division, the result can have no more sig figs than that of the least significant factor.

b) 165 The full result is 165.16, but 21 is uncertain in the unit's place, so the result is uncertain in the unit's place.

Answer 2

a) in multiplication, you keep the # of s.f. of the least accurate value. In this case that would be 3 s.f.

5.18 x 0.0208 = 0.107744 round to 3 s.f. = 0.108

b) in addition, you round to the number of decimals of the least accurate value. In this case that would be 0 decimals places based on the value of 21

21 + 13.8 + 130.36 = 165.16 = 165