Multiplying, dividing and rounding decimals
You can already add and subtract decimals. Three more skills make decimals really useful: multiplying and dividing them by 10, 100 or 1000, multiplying or dividing them by a whole number, and rounding them to the place you need.
Multiply or divide by 10, 100 or 1000
Multiplying a decimal by 10, 100 or 1000 shifts every digit one, two or three places to the left of where it was. Easier to think of it the other way: the decimal point moves to the right.
| Operation | Where the point moves | Example |
| × 10 | 1 place right | 3.47 → 34.7 |
| × 100 | 2 places right | 3.47 → 347 |
| × 1000 | 3 places right | 3.47 → 3 470 |
Dividing does the opposite: the decimal point moves to the left.
| Operation | Where the point moves | Example |
| ÷ 10 | 1 place left | 34.7 → 3.47 |
| ÷ 100 | 2 places left | 347 → 3.47 |
| ÷ 1000 | 3 places left | 3 470 → 3.47 |
If you run out of digits, add a zero. So 5 ÷ 100 isn't a problem — it's 0.05.
Multiply a decimal by a whole number
Three steps, every time:
- Ignore the decimal point and multiply as if both were whole numbers.
- Count the decimal places in the original decimal.
- Place the decimal point in the answer with that many decimal places from the right.
3.4 × 5 → 34 × 5 = 170 → one decimal place → 17.0
0.07 × 6 → 7 × 6 = 42 → two decimal places → 0.42
That last one shows why counting decimal places matters: a tiny number times 6 is still small, and putting the decimal point in the right spot tells you so.
Divide a decimal by a whole number
Set out a normal short-division calculation. Whenever you pass the decimal point in the number you're dividing, bring the point straight up into the answer.
12.6 ÷ 3 → 4.2
7.84 ÷ 4 → 1.96
If a digit doesn't divide cleanly, carry the remainder to the next digit on the right — exactly like with whole numbers.
Rounding decimals
Look at the digit just to the right of the place you're rounding to.
- If it is 0, 1, 2, 3 or 4 → keep the digit as it is and drop the rest.
- If it is 5, 6, 7, 8 or 9 → round the digit up by 1 and drop the rest.
Examples, rounding 3.467:
| Round to | Look at | Result |
| ones | 4 (tenths) | 3 |
| tenths | 6 (hundredths) | 3.5 |
| hundredths | 7 (thousandths) | 3.47 |
Watch out for carries: rounding 4.96 to one decimal place gives 5.0 (not 4.10), because the 9 rounds up to 10 which carries into the ones.
Practice
- ✖️ Multiply and divide decimals by 10, 100, 1000
- ✖️ Multiply a decimal by a whole number
- ➗ Divide a decimal by a whole number
- 🔄 Round decimals