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DECIMALS
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Learn-apply-practise
Decimals
In this section we will look at:
• What is a decimal
• Tenths and hundredths
• How to add, subtract, multiply and divide decimals
• How to change/convert decimals to fractions.
Away back in primary 3 or 4 your teacher would have had you cutting up
oranges and maybe cutting up cakes. In P6 and P7 the teacher probably
“talks” about cutting up Pizzas and dividing bars of chocolate [just before
lunchtime, how considerate]. Well that’s how we start to think about parts of
things. Decimals are simply another way of doing this.
The boss here is always the decimal point. He is like a doorman in a
nightclub, you are not going to move him and he’ll decide what side of the
queue you stand on.
IM THE FULL STOP.
WHOLE NUMBERS TO
THE LEFT, BITS OF A
NUMBER TO THE
RIGHT.
I DON’T CARE IF YOU
KNOW THE
TRANSFERTUTOR
YOURE NOT GETTING
IN…..
The decimal point divides the whole number and parts of a whole number.
16.4
Whole number
part of number
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The decimal point separates the
whole number from the tenths and
hundredths.
Tens
Units
3
1
4
0
5
6
.
.
.
.
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Tenths
1
9
9
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31.1= 31 whole units and 1 tenth of a unit
40.9= 40 whole units and 9 tenths of unit
56.9= 56 whole units and 9 tenths of a
unit.
It’s really useful to think of decimals in terms of money. If you have £10.50 in
your piggy bank, you have 10 whole pounds and you have 5/10’s of a pound.
1/10 of a pound is 10p. 5/10’s is 50 pence.
You could ask your mum if you get all of your practice questions right with
decimals if she would let you practise with a £10 note. Your task is to go and
buy some magazines, sweets and things like that. Its called practical
application, we’ll that’s what we call it.
If mum asks tell her the thetransfertutor told you that you needed practical
experience with decimals.
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1.7
Every number to the left of the
decimal point is a whole
number
Every number to the right of the decimal
point is part of a number
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Thousands
Hundreds
Tens
Units
D
Point
Tenths
Hundredth
s
Cut out the numbers below and make the following decimal numbers
10.25, 3.40, 3.04, 1.24, 5.89
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Thousandths
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LEARN
THE FIRST COLUMN TO THE RIGHT OF THE TENTHS COLUMN IS
TENTHS.
THE SECOND COLUMN TO THE RIGHT OF THE DECIMAL POINT IS
HUNDREDTHS.
HUNDREDTHS
Hundredths are smaller parts of number. Again it can be useful to think of
them in terms of pounds.
1 p is 1/100 of a pound.
As a decimal we write 1 hundredth as 0.01
Try counting up in hundredths: 0.01,
0.02, 0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09, 0.10
0.10 is the same as 0.1
We can say that 0.10 is 1 tenth or also 10 hundredths. They are the same
thing, just represented differently.
To go back to the money comparison [again] it’s just like having 10 1ps in
your pocket or a 10p piece.
You have the same money; it’s just made up differently.
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EXAM TIP
IF YOU ARE ASKED TO FIND A DIGIT WHICH IS WORTH FOR INSTANCE
6 HUNDREDTHS
• First find the decimal point
• Then count across two columns to the right
• Now you’ve found the right column simply find the one which has 6
hundredths
546.70
000.06
345.78
234.89
Now its time for you to do some work
Circle the number below that has a digit worth more than 5 hundredths
1.
2.
3.
4.
5.
23.01
24.78
34.45
34.01
1.10
Ok which one did you pick?
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Well done it was number 2. Remember the question said more than 5
hundredths.
If you have ever heard your teacher or Mum saying you made a “careless
mistake” well if you picked number 3 that’s what adults call a “careless
mistake.”
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ADDING AND SUBTRACTING
DECIMALS
Once you use the correct method you shouldn’t be making mistakes with
adding and subtracting decimals together. I hate to repeat myself, [ well I
don’t really as all teachers/tutors repeat themselves] but you have to practise
these skills and then practise them some more. Sorry!
The key thing to remember is to make sure that the decimal points are lined
up correctly. You will most likely be given the numbers horizontally so the
examiner is testing whether you can lay the sum out correctly.
For instance:
Find the answer to 5.7+ 5.08+6.78+2.34
5.7
5.08
6.78
+ 2.34
Put in a 0 to balance the sum
Then add together as you normally.
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• Always round your numbers to the
nearest whole number and add
mentally to get a rough answer
• Make sure the decimal point is
lined up.
Finally practise and then practise some more adding decimals numbers.
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MULTIPLYING AND DIVIDING
DECIMALS
You may be asked to multiply decimals in your test. To do this:
• Keep your decimal point in line
• Multiply the decimal part of the number
• Then multiply the whole part of the number
• Check your answer
Example:
3
.
5
×
5
1 7 .
5
2
To divide a decimal number
To divide a decimal:
0_. 3_1____
8) 2 . 4 8
____
2
Generally you will have to divide to two decimal places. If you need to round
of the number to TWO decimal places
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How to multiply a decimal by a decimal
There is a simple way to do these types of calculations.
•
•
•
•
IGNORE THE DECIMAL POINT
MUTIPLY THE SUM AS NORMAL
COUNT THE DIGITS AFTER THE DECIMAL PLACE IN BOTH OF
THE NUMBERS YOU HAVE MULTIPLIED
PUT THIS BACK INTO THE ANSWER.
3.74 × 5.3
374 × 53= 19,822
THERE ARE 3 NUMBERS AFTER THE
DECIMAL POINT.
19,822 TAKE THE DECIMAL PLACE IN 3
PLACES = 19.822
PRACTISE THESE:
1.9 × 2.3=
2.6 × 4.7=
3.3 × 7.6=
REMEMBER TO ROUND YOUR
NUMBERS BEFORE YOUR BEGIN TO
MAKE SURE YOUR ANSWER IS
REALISTIC.
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Equivalent fractions, decimals and
percentages
Fractions decimals and percentages are all related to one another. They all
can be changed into the equivalent of the other.
EXAM TIP
In an exam you will generally be asked to find a fraction, decimal or % of an
amount. However there are generally easy questions that simply ask you to
change one to another. You must learn the following:
.
1/2 = 50%= 0.5
1/10 = 10%= 0.1
1/4 = 25%=0.25
1/100 = 1%=0.01
3/4=75%=0.75
1/5= 20%=0.2
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If you know these then you can work out other problems
If 1/5 = 0.2
Then 2/5 = 0.4
If 1/100 = 0.01
Then 18% = 0.18
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Converting
Converting means changing. It’s like going to the bureau de change to
convert pounds to euros. Unfortunately for us the Euro has been so poor we
haven’t really had many opportunities to do this. So that gives an extra
incentive to practice here, unless of course you have a cousin from Dundalk
or Donegal. Ask them to help you with conversions; they know more than
even thetransfertutor. [Well that’s stretching it]
So how do we do it?
Learn the following
To change a decimal to a percentage
MULTIPLY BY 100
0.50 × 100 = 50%
To change a percentage to a decimal
DIVIDE BY 100
45% = 0.45
To change a fraction to a decimal
DIVIDE THE TOP NUMBER BY THE BOTTOM NUMBER
__0_._7__5_
¾ = 0.75 4 ) 3. 30 20
To change a percentage to a fraction
This one is easy, simply put 100 underneath
64%= 64
100
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Now try to apply these ideas. Repeat, repeat, repeat until
you can do all three.
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