Question

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

(a) 0.436

(b) 9.000

(c) 27.2

(d) 135

(e) 1.497 × 10^-3

(f) 0.445

Short answer

a) 0.44

b) 9.0

c) 27

d) 140

e) 1.5 x10^-3

f) 0.45

Step-by-step solution

Rules to determine the significant figures in a number:

1. Non-zero digits are usually important.
2. Any zeros between the first and second significant digits are significant.
3. Only the last zero or trailing zeros in the decimal section are significant.
4. 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 0.436 up to two significant figures will be 0.44.

b) Rounding off the number 9.000 up to two significant figures will be 9.0.

c) Rounding off the number 27.2 up to two significant figures will be 27.

d) Rounding off the number 135 up to two significant figures will be 140.

e) Rounding off the number 1.497×10^-3 up to two significant figures will be 1.497×10^-3.

f) Rounding off the number 0.445 up to two significant figures will be 0.45.