Decimals
Line up, multiply, and divide decimals without losing the point.
Best in your head · no pen, no calculator why?
Opens at level 7. You're level 1. You can read and practice here now.
the idea
A decimal is a fraction with 10, 100 or 1,000 on the bottom: 0.3 is three tenths, and 0.25 is twenty-five hundredths. The decimal point marks where the whole numbers end.
Almost every decimal slip is a place-value slip. To add or subtract, line up the points so tenths meet tenths. To multiply or divide, work with whole numbers first, then put the point back where the size says it belongs. A rough estimate tells you whether the answer should be about 2, 20 or 200.
techniques
Line up the points
- Write the numbers with their decimal points lined up.
- Fill any gap with a zero, so 3.4 becomes 3.40.
- Add or subtract as if they were whole numbers, and keep the point in place.
worked example
6.3 − 2.45
- Line them up: 6.30 − 2.45.
- 630 − 245 = 385, so the answer is 3.85.
Answer: 3.85
Multiply, then place the point
- Leave out the points and multiply the whole numbers.
- Count the decimal places in the two numbers together.
- Give the answer that many decimal places, then drop any zeros at the end after the point.
worked example
0.75 × 8
- 75 × 8 = 600.
- 0.75 has two decimal places, so 6.00, which is 6.
Answer: 6
Clear the decimals, then divide
- If the divisor, the number you divide by, has a point, multiply both numbers by 10.
- Repeat until the divisor is whole. The answer doesn't change, since both numbers grew by the same factor.
- Only the first number has a point? Divide as whole numbers, then give the answer that many decimal places.
- Check the size: dividing by a number below 1 gives a bigger answer.
worked example
4.8 ÷ 0.6
- Multiply both by 10: 48 ÷ 6.
- 48 ÷ 6 = 8.
Answer: 8
watch out for
- Lining up the last digits instead of the points. 3.4 + 2.15 is 5.55; treating 3.4 as 0.34 gives 2.49.
- Forgetting to put the point back after multiplying. 2.5 × 8 is 20, not 200.
- Placing the point by guesswork. 7.2 ÷ 0.9 is 8, not 0.8, because dividing by a number below 1 makes the answer bigger.
practice
Add & subtract decimals
worked example
16.4 − 10.71
Answer: 5.69
- Line up the decimal points: 16.40 − 10.71 = 5.69.
Multiply decimals
worked example
2.5 × 4
Answer: 10
- Do 25 × 4 = 100 without the point, then put one decimal place back: 10.0, which is 10.
Divide decimals
worked example
1.8 ÷ 6
Answer: 0.3
- 1.8 is 18 ÷ 10, and 18 ÷ 6 = 3.
- So the answer is 3 ÷ 10 = 0.3.