Problem 57P

Perform each calculation to the correct number of significant figures.

(a) 4.5 × 0.03060 × 0.391

(b) 5.55 ÷ 8.97

(c) (7.890 × 1012) ÷ (6.7 × 104)

(d) 67.8 × 9.8 ÷ 100.04

Solution 57P

Step 1:

First let’s see the rules for significant numbers :

- All non-zero digits are considered significant. For example, 81 has two significant figures- 8 and 1, while 123.45 has five significant figures -1, 2, 3, 4 and 5.
- Zeros appearing anywhere between two non-zero digits are significant.

Example: 101.1203 has seven significant figures: 1, 0, 1, 1, 2, 0 and 3.

- Leading zeros are not significant. For example, 0.00052 has two significant figures: 5 and 2.
- Trailing zeros in a number containing a decimal point are significant. For example : 12.2300 has six significant figures: 1, 2, 2, 3, 0 and 0. The number 0.000122300 still has only six significant figures (the zeros before the 1 are not significant). In addition, 120.00 has five significant figures since it has three trailing zeros.

Rules for Rounding Off :

1. If the first digit to be dropped is 4 or less, then it and all following digits are simply dropped from the number.

2. If the first digit to be dropped is 5 or greater, then the last retained digit of the number is increased by 1.