Understanding decimals
A decimal uses a point to show parts smaller than one. In 3.47 the digit 4 is tenths and 7 is hundredths. Decimals can be positive or negative, and the same sign rules as integers apply to −2.5, −0.8 and so on.
Key idea / Key idea
To add or subtract decimals, line up the decimal points and work in columns. To multiply, ignore the points first, then count the total decimal places. To divide, make the divisor a whole number by shifting both points.
Comparing decimals
Compare digit by digit from the left, starting with the whole-number part and then the tenths, hundredths, and so on. Adding zeros to the right of the last digit does not change a decimal, so 0.5 = 0.50, which makes columns easier to line up. For negatives, the one closer to 0 is larger, so −0.3 > −0.9. On a number line −1.2 sits between −1 and −2.
Worked example / Worked example
Calculate −3.6 + 1.25.
Different signs, so subtract: 3.60 − 1.25 = 2.35.
Keep the sign of the larger number (−3.6), giving −2.35.
Multiplying and dividing decimals
Multiply as if there were no points, then place the point so the answer has as many decimal places as the two numbers together. For division, shift both points the same number of places to make the divisor whole.
- 0.4 × 0.6 = 0.24 (two decimal places)
- −1.2 ÷ 0.3 = −4 (shift both points one place: −12 ÷ 3)
Remember / Remember
- Line up decimal points when adding or subtracting.
- Count decimal places when multiplying.
- Sign rules are the same as for integers.