# Dividing Decimals

How do we divide when there are decimal points involved?

Well, it is easier to divide by a whole number ... so multiply by 10 until it is!

But we must do the same thing to both numbers in the division.

### Example: 15 divided by 0.2

When we multiply the 0.2 by 10 we get a whole number:

0.2 × 10 = 2

But we must also do it to the 15:

15 × 10 = 150

So 15 ÷ 0.2 has become 150 ÷ 2 (both numbers are 10 times larger):

150 ÷ 2 = 75

And so the answer is:

15 ÷ 0.2 = 75

The number we divide by is called the divisor.

To divide decimal numbers:

Multiply the divisor by as many 10's as we need, until it is a whole number.
Remember to multiply the dividend by the same number of 10's.

Multiplying by 10 is easy, we just shift one space over like this:

### Example: Divide 6.4 by 0.4

Let us move one space for both:

 move 1 6.4 → 64 0.4 → 4 move 1

6.40.4 is exactly the same as 644
as we did the move for both numbers.

Now we can calculate:

644 = 16

So the answer is:

6.40.4 = 16

Are there really 16 lots of 0.4 in 6.4? Let's see:

For harder questions we may need to use Long Division:

### Example: Divide 0.539 by 0.11

First we need to make the move twice to make 0.11 into a whole number:

 move 2 spaces 0.539 → 5.39 → 53.9 0.11 → 1.1 → 11 move 2 spaces

0.5390.11 is exactly the same as 53.911

But what about 53.9? It still has a decimal point.

Well, we can ignore the decimal point in the dividend so long as we remember to put it back later.

First we do the calculation without the decimal point:

 049 11)539    0    53    44     99     99      0

Now put the decimal point in the answer directly above the decimal point in the dividend:

 04.9 11)53.9

The answer is 4.9

Another example:

### Example: Divide 9.1 by 7

The divisor (7) is already a whole number, so no need for any moves.

Now, ignore the decimal point in the dividend and use Long Division:

 13 7)91   7   21   21    0

Put the decimal point in the answer directly above the decimal point in the dividend:

 1.3 7)9.1

The answer is 1.3

## Animations

Have a look at these Decimal Division Animations for further help.

## Lastly ...

As a final check we can put our "common sense" hat on and think "is that the right size?", because we don't want to pay ten times too much for anything, nor do we want to get only one-tenth of what we need!

965, 1351,966, 1352,967, 1353, 3467, 3468, 3469, 3470