Decimal Fractions and Decimal Operations
Decimal fractions use place value based on powers of ten. They are useful for money, measurement, estimation and scientific quantities.
Place value and comparison
To the right of the decimal point are tenths, hundredths, thousandths and so on. Compare decimals by aligning decimal points and adding zeros where necessary: 0.70 = 0.7.
Operations and conversion
- Align decimal points before adding or subtracting.
- For multiplication, multiply as whole numbers and place the decimal point using the total number of decimal places.
- To convert a fraction to a decimal, divide numerator by denominator; to convert a terminating decimal to a fraction, use its place-value denominator.
Rounding and standard form
To round, inspect the next digit: 5 or more increases the retained digit by one; 4 or less leaves it unchanged. Standard form is A × 10ⁿ, where 1 ≤ A < 10.
Worked examples and practice
- 3.45 + 0.8 = 4.25.
- 0.6 × 0.04 = 0.024.
- 0.375 = 375/1000 = 3/8; 4,560,000 = 4.56 × 10⁶.
- Round 7.846 to 2 decimal places and 0.004982 to 2 significant figures.
