Decimals Summary
Academic Skills Advice
A decimal number comes after the decimal point and tells you what fraction (small part) you
have.
6
3.6
means 3 whole ones and 10.
3.06
means 3 whole ones and 100.
6
6
3.006 means 3 whole ones and 1000 etc
Multiplying Decimal Numbers by 10, 100 & 1000.


move the decimal point to the right.
x10 move 1 place, x100 move 2 places, x1000 move 3 places etc
27.36 x 10 = 273.6
Dividing Decimal Numbers by 10, 100 & 1000.


move the decimal point to the left.
÷10 move 1 place, ÷100 move 2 places, ÷1000 move 3 places etc
47.85 ÷ 1000 = 0.04785
Adding and Subtracting Decimals:


Line up the decimal point
Add or subtract as normal
Add 28.7 and 4.62
Make sure you line the decimal point up then just add as normal.
28.7
4.62
33.32
Multiplying Decimals:



Ignore the decimal points and any zeros at the beginning or end of the numbers.
Multiply the numbers as normal.
Decide where to put the decimal.
Work out 2.542 x 0.02
Ignore the decimal points and do 2542 x 2 = 5084.


Now count how many numbers came after a decimal point in the question: 2.542 x 0.02
(there are 5 numbers after a decimal point: 5,4,2,0,2 (ticked) so you need to move the
decimal point back 5 places so there are 5 numbers after the decimal point in your answer:
0.05084 (check your answer by counting how many numbers are after the point)
© H Jackson 2010 / Academic Skills
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Dividing 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.
Divide as normal.
Work out 5.16 ÷ 0.2
(we want to divide by 2, not 0.2 so x both bits by 10).
25.8
2)51.6
Work out 4.8 ÷ 0.03
(we want to divide by 3, not 0.03 so x both bits by 100).
160
3)480
Nb. You do not need to do anything to convert your answer – it is the final answer.
Rounding to a Certain Number of Decimal Places:

Look at the next number after the one you want to stop at.
o 5 or above – round up
o Less than 5 – stays the same
Round 22.585 to 2 decimal places.
You want the number
to stop here.
Look at the next number (5). It
is 5 or above so round the 8 up.
22.585
Answer is 22.59
Round 89.7714 to 3 decimal places.
You want the number
to stop here.
89.7714
Look at the next number (4).
It is less than 5 so the 1 stays
the same.
Answer is 89.771
Nb. Never move the decimal point. Never round down.
© H Jackson 2010 / Academic Skills
2