Multiplying and Dividing DECIMALS
1) Multiplying and dividing by 10, 100, 1000
You need to learn the following rules:
Action
Rule
Example
Multiply by 10
Move the decimal point one place to the right
2.45 x 10 = 24.5
Multiply by 100
Move the decimal point two places to the right
2.45 x 100 = 245
Multiply by 1000 Move the decimal point three places to the right 2.45 x 1000 = 2450
Divide by 10
Move the decimal point one place to the left
46.7 ÷ 10 = 4.67
Divide by 100
Move the decimal point two places to the left
46.7 ÷ 100 = 0.467
Divide by 1000
Move the decimal point three places to the left
46.7 ÷ 1000 = 0.0467
Question 1
What is:
a) 6.23 x 1000
b) 5.1 ÷ 100
The Answer
a) 6230
b) 0.051
2) Multiplying decimals
Multiplying decimals is the same as multiplying two whole numbers. You just need to remember the following:
If there is one digit after the decimal point in the question, there will be one digit after the decimal point in the
answer.
If there are two digits after the decimal point in the question, there will be two digits after the decimal point in the
answer etc.
Example
3.42 × 2
Solution
Calculate 342 × 2:
There are two digits after the decimal point in the question (3.42 x 2), so there will be two digits after the decimal
point in the answer. Therefore 342 × 2 = 6.84
Question 2
What is 1.2 x 1.1?
The Answer
First work out 12 x 11 = 132
Now count the digits behind decimals points in the question. There are two of them. So you need two digits
behind the decimal point in your answer. So 1.2 x 1.1 = 1.32
3) Dividing decimals
When dividing a decimal by a whole number, divide as usual but keep the decimal points aligned!
For example:
5.75 ÷ 5 =
(Note that the decimal points are in the same place.)
If you are dividing a decimal by another decimal, you need to use equivalent fractions.
For example, 2.42 ÷ 0.2 means
3.715 ÷ 0.005 means
which is the same as
which is the same as
(we have multiplied the top and bottom by 10)
(we have multiplied the top and bottom by 1000)
Remember to always multiply the top and bottom by the same number. And make sure that the bottom is a whole
number.
Worked example
What is 425 ÷ 0.25?
Solution
450 ÷ 0.25 =
=
=
= 1800
(Multiply top and bottom by 100.)
(you can factorise 25 as being 5 x 5, therefore rather than 45000 ÷ 25, simply ÷ by
each factor e.g. 45000 ÷ 5 = 9000 & 9000 ÷ 5 = 1800)