Number System: Dividing Decimals

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 you want to divide by a Decimal Number?
The trick is to convert the number you are dividing by to a whole number first, by shifting the decimal point of both numbers to the right:

Now you are dividing by a whole number, and can continue as normal.
It is safe to do this if you remember to shift the decimal point of both numbers the same number of places.

Example: Divide 6.4 by 0.4

You are not dividing by a whole number, so you need to move the decimal point so that you 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 you moved the decimal point of both numbers.

And the answer is:

64 / 4 = 16

You can see for yourself how many 0.4s make 6.4:

Example: Divide 5.39 by 1.1

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

move 1
5.39		53.9
1.1		11
move 1

You are now dividing by a whole number, so you 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 you can put your "common sense" hat on and think "is that the right size?", because you don't want to pay ten times too much for anything, nor do you want to get only one-tenth of what you need!

Posted in: Dividing Decimals, Number System