Fractions, Decimals and Percentages are a very important part of our number system.
They are three different ways in which we can represent numbers
A fraction is any part of a group, number or whole.
A decimal is a number containing both an integer part and digits seperated by the decimal point
A percentage is a quantity out of 100
It is possible to convert between Fractions, Decimals and percentages. Some key fractions and percentages that you will need to learn are on the next page, followed by how to convert between Fractions, Decimals and Percentages
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Key Fractions, Decimals and Percentages Fraction
Decimal
Percentage
1
2
0.5
50%
1
4
0.25
25%
1
5
0.2
20%
1
10
0.1
10%
1
3
0.333
33.3%
1
8
0.125
12.5%
1
9
0.111
.
.
11.1%
You MUST know all the red ones by Year 6 and ALL of the above in KS3 (Y7 onwards)
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Converting fractions to decimals and percentages Fractions mean to DIVIDE!!
e.g 4 means 4 ÷5
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Now that we know this, we can use it to help us convert a fraction to a decimal.
e.g convert 3 to a decimal
8
This means 3 ÷ 8
0. 3 7 5
3 6 4
8 3. 0 0 0 so we calculate This shows us that 3 is equal to 0.375
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We convert any decimal to a percentage by MULTIPLYING BY 100
so 0.375 x 100 = 37.5%
So now we know that 3 = 0.375 = 37.5%
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Converting between decimals and percentages To convert a DECIMAL to a PERCENTAGE we multiply the decimal by 100
e.g 0.07 = 7%
0.37 = 37%
2.37 = 237%
To convert a PERCENTAGE to a DECIMAL we divide the percentage by 100
e.g 95% = 0.95
6% = 0.06
125% = 1.25
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Terminating and recurring decimals
A terminating decimal is one which ends, it has a final digit
e.g 0.2 or 0.35 or 0.375
A recurring decimal is one in which the digits go on forever, following a pattern.
e.g 0.333333 is a recurring decimal
0.545454 is a recurring decimal
0.354354354 is a recurring decimal
You put the dot(s) above the first and last digits in the pattern to show that you understand that it is recurring
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Converting a terminating decimal into a fraction
We use the following method to convert a terminating decimal to a fraction.
e.g1 what is 0.459 as a fraction?
We look at the last digit in this decimal
0.459 the 9 is in the 'thousandths' column so our denominator in our fraction is going to be a thousand.
We now just imagine that the decimal point has disappeared
Answer = 0459 = 459 1000 1000
The place value heading for the final digit tells you what to put for the denominator of the fraction.
e.g2 Convert 0.85 to a fraction in its simplest form
The last digit is a 5 and it is in the 'hundredths' column so we get the following:
85 100
The numerator and denominator are both in the 5 times tables so dividing them both by 5 we get:
÷5
85 = 17
100 20
÷5
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Converting a recurring decimal to a fraction A recurring decimal is one in which the digits go on forever, following a pattern.
e.g 0.333333 is a recurring decimal
0.545454 is a recurring decimal
0.354354354 is a recurring decimal
You put the dot(s) above the first and last digits in the pattern to show that you understand that it is recurring
To convert a recurring decimal we can do the following:
e.g write 0.844844844 as a fraction
This decimal has a 3 digit pattern, so we put these 3 digits over 3 nine's to turn it into a fraction.
Answer = 844
999
To put it simply, you need to count the number of digits that are recurring in the decimal and this tells you how many nines to put as the denominator.
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Converting top heavy fractions to mixed numbers
a top heavy (improper) fraction is one where the numerator is bigger than the denominator.
e.g 15 4
A top heavy fraction is always LARGER THAN 1
We can convert a top heavy fraction into a mixed number.
e.g convert 15 into a mixed number
4
15 means 15 ÷ 4
4
0 3 r3 3
4
1
4 1 5 = 3 4
A mixed number is a MIXTURE of a whole number and a fraction!!
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Converting a mixed number to a top heavy (improper) fraction
To change a mixed number into an improper fraction you use the following method:
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e.g write 5 as an improper fraction
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First step: MULTIPLY the whole number by the denominator
5 x 8 = 40
This shows us that 5 = '40 eighths'
Last step: ADD the numerator to your answer to step 1
3 + 40 = 43
3
This tells us how many 'eighths' that 5 is equal to
8
Answer = 43
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