Question

Round off each of the following numbers to two significant figures:

(a) 517

(b) 86.3

(c) 6.382 ×10³

(d) 5.0008

(e) 22.497

(f) 0.885

Short answer

a) 520

b) 86

c) 6.4 x10³

d) 5.0

e) 22

f) 0.89

Step-by-step solution

Rules to determine the significant figures in a number:

a) Non-zero digits are usually important.

b) Any zeros between the first and second significant digits are significant.

c) Only the last zero or trailing zeros in the decimal section are significant.

d) Leading zeros, i.e., zeros which come before the decimal point and any non-zero digit, are insignificant

Definition of significant figure:

Significant figure is the number of significant single digits in the coefficient of an expression, referred to the accuracy of measurement. The number of significant figures in a statement shows the degree of certainty or precision with which an engineer or scientist states a number.

Rules regarding rounding off:

If a rounding number is followed by 5,6,7,8,9, then the number needs to be round up. If a rounding number is followed by 0,1,2,3,4, then the number needs to be round down.

Rounding off numbers

a) Rounding off the number 517 up to two significant figures will be 520.

b) Rounding off the number 86.3 up to two significant figures will be 86.

c) Rounding off the number 6.4 x10³ up to two significant figures will be 6.4 x10³.

d) Rounding off the number 5.0008 up to two significant figures will be 5.0.

e) Rounding off the number 22.497 up to two significant figures will be 22

f) Rounding off the number 0.885 up to two significant figures will be 0.89.