Rounding Small Decimal Numbers to Significant Figures

Topic Content:

The number 0 . 000 765 has 6 decimal places. The zero before the decimal number means that there are no units, and the three zeros after the decimal point mean that there are no tenths, no hundredths, and no thousandths, so the four zeros are not significant or the first significant figure.

Therefore, the most significant or first significant figure is 7. The second significant figure is 6, and the third significant figure is 5.

Note: the first significant figure is always the first non-zero figure as you read a number from the left.

Worked Example 12.5.1:

Round off 0.000765 correct to:

i. 1 S.F.
ii. 2 S.F.
iii. 3 S.F.

Solution

i. 0.000765 = 0.0008 correct to 1 S.F.

ii. 0.000765 = 0.00077 correct to 2 S.F.

iii. 0.000765 = 0.000765 correct to 3 S.F.

Worked Example 12.5.2:

Round off 0.04829 correct to:

i. 1 S.F.
ii. 2 S.F.
iii. 3 S.F.

Solution

i. 0.04829 = 0.05 correct to 1 S.F.

ii. 0.04829 = 0.048 correct to 2 S.F.

iii. 0.04829 = 0.0483 correct to 3 S.F.

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