Download Multiplying Decimals

Academic Skills Advice
Decimals
Multiplying Decimal Numbers by 10, 100 & 1000.
When you multiply a number by 10, 100, 1000 etc the numbers all move up to the next
place value column and so it looks like the decimal point has moved. (Try 27.34 x 10 on a
calculator and see what happens.)
The easy way to multiply by 10, 100, 1000 etc is to move the decimal point to the right.
Look at the number of 0’s to see how many places to move the point. (e.g. x10 move 1
place, x100 move 2 places, x1000 move 3 places etc.)
34.52 x 10 = 345.2
(the decimal “jumps over” 1 number to the right)
34.52 x 100 = 3452
(the decimal “jumps over” 2 numbers to the right)
34.52 0 x 1000 = 34520
(the decimal “jumps over” 3 numbers to the right)
Notice that when you multiply by 10, 100, 1000 etc the digits all stay the same it is just
their position in relation to the decimal point that changes.
Also notice when multiplying by 1000 there were only 2 numbers to jump over so a 0 had
to be added.
Dividing Decimal Numbers by 10, 100 & 1000.
This is exactly the same principle as multiplying decimal numbers except that the decimal
point now moves to the left.
34.52 ÷ 10 = 3.452
(the decimal “jumps over” 1 number to the left)
34.52 ÷ 100 = 0.3452
(the decimal “jumps over” 2 numbers to the left)
34.520 ÷ 1000 = 0.03452
(the decimal “jumps over” 3 numbers to the left)
Once you have decided where the decimal point should go always check that it is in the
correct place by thinking about where it started and how many places it has moved.
If you are not sure whether to move the point left or right remember: when you multiply the
number should end up bigger, and when you divide the number should end up smaller.
© H Jackson 2010 / ACADEMIC SKILLS
1
Adding and Subtracting Decimals:
When adding or subtracting decimal numbers be careful to line up the decimal point then
just add or subtract as normal.
Example:

+

-
Add 13.4 and 8.75
Line the decimal point up then add as normal.
13.40
8.75
22.15
Work out 27 – 5.32
Line the decimal point up then subtract as normal.
27.00
5.32
21.68
Notice that 2 zero’s have been added to the 27, after the
decimal point, to make it easier to line the numbers up.
Multiplying Decimals:
To multiply decimal numbers:
 Remove the decimal points
 Multiply the numbers as normal
 Decide where to put the decimal point.
(To do this count how many numbers came after a decimal point in the question (i.e. the
total number of decimal places) and you need the same amount after the decimal point in
the answer.)
Examples:

Work out 1.342 x 0.03
Remove the decimal points and multiply:
1342 x 3 = 4026.


Count how many numbers came after a decimal point in the question: 1.342 x 0.03
(there are 5 numbers after a decimal point: 3,4,2,0,3 (ticked))
You need to move the decimal point back 5 places:
(so there are 5 numbers after the decimal point in your answer)
0.04026
(check your answer by counting how many numbers are after the decimal point)

Work out 35 x 1.32
Remove the decimal points and do 35 x 132 = 4620.
Now put the decimal point in the correct place and the answer is 46.20
© H Jackson 2010 / ACADEMIC SKILLS
2
Dividing with Decimal Numbers:
Dividing into a decimal number is straightforward. Just divide as normal keeping the
decimal point lined up in your answer.
Example:

Work out 57.6 ÷ 3
Divide one number at a
time and put your answer
on the answer line.
19.2
3)57.6
Line the decimal point up in the answer.
Dividing by a decimal number can be difficult without a calculator so we use a method
which changes the calculation into one where we divide by a whole number:
To divide by a decimal number:
 Multiply the decimal by 10, 100 or 1000 to make it into a whole number.
 Do exactly the same to the number you are dividing into.
(see page 1 for how to multiply by 10, 100 or 1000.)
 Divide as normal.
Examples:

Work out 7.14 ÷ 0.3 (we want to divide by 3, not 0.3 so x both bits by 10).
(Now we have 71.4 ÷ 3)
23.8
3)71.4
You don’t need to make any adjustments – this is the final answer.

Work out 6.3 ÷ 0.02 (we want to divide by 2, not 0.02 so x both bits by 100).
(Now we have 630 ÷ 2)
315
2)630
(if you’re not sure – check these on a calculator)
© H Jackson 2010 / ACADEMIC SKILLS
3