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.
