Decimals, Estimation, Approximation and Significant Figures
Decimals can be calculated exactly or approximated to a stated degree of accuracy.
Place value and operations
Align decimal points for addition and subtraction. In multiplication, count decimal places in the factors. In division, make the divisor a whole number by shifting both decimal points equally.
Approximation
Rounding to decimal places keeps a fixed number of digits after the decimal point. Significant figures begin at the first non-zero digit and count meaningful digits thereafter. Estimation replaces values by convenient approximations to check reasonableness.
Worked examples
- 7.846 rounded to 2 decimal places is 7.85.
- 0.004982 to 2 significant figures is 0.0050 or 5.0 × 10⁻³.
- 49.8 × 2.02 is approximately 50 × 2 = 100.
Practice
- Round 12.496 to 1 and 2 decimal places.
- Give 0.000736 to 2 significant figures.
- Estimate 398 ÷ 19.6 and compare with the calculator value.
