Decimal Operations
What you must know
Decimal questions require placing the decimal point correctly in addition, subtraction, multiplication, and division, plus converting between decimals, fractions, and percents. Understand place value: each place to the right of the decimal is tenths, hundredths, thousandths, and so on.
Common traps
- Alignment in addition/subtraction: Line up decimal points before computing. 3.5 + 0.42 = 3.92, not 3.47.
- Multiplication decimal placement: Multiply as if whole numbers, then count the total decimal places in both factors. 0.4 × 0.3 = 0.12 (two decimal places).
- Division: Move the decimal in the divisor to make it a whole number, and move the dividend's decimal the same number of places. 1.2 ÷ 0.4 becomes 12 ÷ 4 = 3.
- Trailing zeros: 0.50 equals 0.5, but 0.05 does not. Watch zeros between the decimal and a digit.
- Rounding: Round to the requested place; look at the next digit (5 or more rounds up).
Worked example
Multiply 2.5 × 0.04. Multiply 25 × 4 = 100. Count decimal places: one in 2.5 and two in 0.04 gives three, so the answer is 0.100 = 0.1.
Rule of thumb
For multiplication, count total decimal places in the factors and place them in the product. For division, make the divisor a whole number first.