How to divide by a decimal by scaling both numbers

Cut 4.2 metres of ribbon into pieces that are each 0.2 metre long. Division asks how many pieces fit. Count both lengths in tenths of a metre: the ribbon has 42 tenths, and each piece has 2 tenths. The pieces have not changed size.

Move both decimal points

Multiply both numbers by ten to get 42 and 2. The answer stays at twenty-one.

4.2× 10 ↓42

0.2× 10 ↓2

Count the same ribbon in a new unit

How many 0.2-metre pieces fit in 4.2 metres?

Use tenths for both lengths

$4.2\div0.2=42\div2$

Multiply both numbers by ten. You now count tenths instead of metres. Changing both keeps the number of pieces fixed.
Work out the group count

$42\div2=21$

Forty-two tenths contain twenty-one groups of two tenths. So the ribbon makes twenty-one pieces.
Rebuild the starting length

$21\times0.2=4.2$

The pieces together make the full ribbon. Multiplying back checks that you kept the same group count.

Choose how far to scale

The divisor is the number you divide by. Make it whole by multiplying by 10, 100 or another power of ten. Use the same factor for the other number.

For 3.5 ÷ 0.25, multiply both by 100. You get 350 ÷ 25 = 14. Multiplying by ten would leave 2.5 as the divisor, so it would not finish the job.

Changing only the divisor changes the size of each group. That changes how many fit. You also cannot divide by zero.

A larger answer can make sense

The ribbon was only 4.2 metres, but it makes 21 small pieces. The answer counts pieces rather than metres. Dividing by a number below one can give a larger number for that reason.

Try it yourself

Work out an answer and explain your reasoning. Then check the explanation.

Clear hundredths from the divisor

$1.2\div0.04$

How many groups fit? Choose the scale factor yourself, then find the answer.

Show the answerHide the answer

$120\div4=30$

Multiply both numbers by one hundred. Then divide 120 by 4.

Change both numbers in the same way

$6.3\div0.3=6.3\div3$

One number changed and the other did not. Repair the division and find the actual count.

Show the answerHide the answer

$63\div3=21$

Changing only the divisor makes each piece ten times larger. Multiply 6.3 by ten too.

When a decimal answer keeps going

The method is exact even when the answer repeats. For 1 ÷ 0.3, use 10 ÷ 3. The answer is 3.333… rather than a decimal that ends. This practice game uses answers that end.

Choose a new unit yourself

Try decimal division with exact answers that end. Choose enough tens to make the divisor whole, change both numbers and check the count.

2-minute practice · keep going after mistakes · opens in a new tab

Try decimal division