Dividing Decimals

Quick method: use Long Division without the decimal point,
then re-insert the decimal point in the answer.

Dividing a Decimal Number by a Whole Number

To divide a decimal number by a whole number:

  • Use Division or Long Division (ignoring the decimal point)
  • Then put the decimal point in the same spot as the dividend (the number being divided)

 

Example: Divide 9.1 by 7

Ignore the decimal point and use Long Division:

   13
7 )91
   9
   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

Dividing by a Decimal Number

But what if we want to divide by a Decimal Number?

The trick is to change the number we are dividing by to a whole number first, by shifting the decimal point of both numbers to the right:

move decimals

Now we are dividing by a whole number, and can continue as normal.

It is safe to do this if we remember to shift the decimal point of both numbers the same number of places.

Example: Divide 6.4 by 0.4

We are not dividing by a whole number, so we need to move the decimal point so we are dividing by a whole number:

move 1
6.4 64
0.4 4
move 1

6.4/0.4 is exactly the same as 64/4,
as we moved the decimal point of both numbers.

Now we can calculate:

64 / 4 = 16

So the answer is:

6.4 / 0.4 = 16

 

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


Example: Divide 5.39 by 1.1

Move the decimal point so that we are dividing by a whole number:

move 1
5.39 53.9
1.1 11
move 1

We are now dividing by a whole number, so we can proceed:

Ignore the decimal point and use Long Division:

    049
11 )539
    5
    0
    53
    44
     99
     99
      0

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

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!