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In order to access this I need to be confident with:
Equivalent fractions Ordering fractions Decimal number line To the power ofThis topic is relevant for:
Here we will learn about converting fractions, decimals and percentages, including how to define a fraction, a decimal and a percentage, convert between fractions, decimals and percentages and compare and order them.
There are also converting fractions, decimals and percentages worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if youβre still stuck.
In order to compare fractions, decimals and percentages you need to be able to convert between them. On this page we will explore how to convert between fractions, decimals and percentages step by step with examples.
Here is a summary
Fractions, decimals and percentages are different ways of expressing the same value
Fraction:
means
The numerator refers to how many βpartsβ we have and the denominator refers to how many βpartsβ there are in total. So here we have 1 out of 4 parts.
We need to equate denominators when converting fractions.
can be verbalised as βthree out of eightβ or βthree eighthsβ.
is known as βone quarterβ.
Note: The line in a fraction is called the vinculum.
Note: Any value that can be written as a fraction is called a βrational number.β
Decimal:
Numbers containing a decimal point are often referred to as βdecimalsβ.
E.g.
Note: The word decimals comes from the Latin decima meaning a tenth. This is why the numbers after the point represent βtenthsβ, βhundredthsβ and so on.
Percentage:
A percentage represents a number out of
E.g.
Note: The
Fractions, decimals and percentages are all equivalents of each other, so we can order them by converting them into the same form.
E.g.
Write these numbers in ascending order.
Converting the fractions and decimals to percentages gives
Ascending means smallest to biggest, the smallest percentage is 19% = 0.19, the biggest percentage is 30% = 0.3.
In ascending order
Letβs explore below how we can convert between fractions, decimals and percentages.
In order to compare fractions, decimals and percentages you need to be able to convert between them. Here we will explore step by step how to convert between the following:
In order to convert a fraction to a decimal:
Divide the numerator by the denominator.
E.g.
(Use a written method or a calculator)
Step by step guide: Fraction to decimals
In order to convert a decimal to a fraction in its simplest form:
E.g.
Step by step guide: Decimals to fractions
In order to convert a fraction to a percentage:
E.g.
Or:
E.g
Step by step guide: Fractions to percentages
In order to convert a percentage to a fraction:
E.g.
Step by step guide: Percentages to fractions
In order to convert a decimal to a percentage:
Multiply the decimal by a
E.g.
Step by step guide: Decimals to percentages
In order to convert a percentage to a decimal:
Divide the percentage by
E.g.
Step by step guide: Percentages to decimals
In order to convert a recurring decimal to fraction:
E.g.
Step by step guide: Recurring decimals to fractions
In order to compare fractions, decimals and percentages:
Get your free comparing fractions, decimals and percentage worksheet of 20+ questions and answers. Includes reasoning and applied questions.
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DOWNLOAD FREEKey terminology for converting fractions, decimals and percentages
Integer
A whole number
E.g.
Comparing
Examining the differences between two or more items/values.
Equivalent fraction
Fractions that are of the same value but shown differently
E.g.
Therefore,
are equivalent fractions.
Unit fraction
A fraction with 1 as its numerator is sometimes called a βunit fractionβ:
E.g.
is a unit fractions because its numerator is
Unlike denominators
Fractions with non-identical denominators are sometimes called unlike denominators. When comparing fractions we need a common denominator (sometimes called like denominators):
E.g.
are unlike denominators because the bottom numbers of each fractions are not the same.
Improper fraction
A fraction where the numerator is greater than the denominator
E.g.
Mixed number
A number made up of an integer and a fraction
E.g.
Convert
To change between one form and another
E.g.
Recurring decimal
A decimal number with a digit (or group of digits) that repeats forever. The part that repeats can also be shown by placing dots over the first and last digits of the repeating pattern:
E.g.
Note: this are sometimes called repeating decimals
Ascending order
Increasing in value.
Descending order
Decreasing in value.
Place these fractions and decimals in ascending order:
As the two of the values are all fractions so we can convert the single decimal to fraction form.
2Convert all the fractions so they have a common denominator.
As you are comparing fractions you need to find a common denominator for the three fractions, we can do this by finding the lowest common multiple of
Therefore the common denominator is
Letβs now convert each fraction to have a denominator of
3Compare the numerators (denominators must be equal).
As the fractions now have a common denominator we can compare the different numerators:
4Check you have answered the question e.g. are they in ascending order?
The ascending order is:
5Write all values in their original form.
The fractions and decimals in ascending order are:
Place these in descending order:
Convert all the values into the same form: fractions, decimals or percentages.Β
Three of the values are decimals and one is a percentage so we can convert the single percentage to a decimal.
Write all values in a vertical line ensuring the decimals places are aligned.
The best way to compare decimals is to write all values in a vertical line ensuring the decimals places are aligned (see below):
Compare the units, tenths, hundredths etc.
Create a place value table and put each number in:
Units | Decimal Point | Tenths | Hundredths | Thousandths |
0 | . | 7 | ||
0 | . | 7 | 7 | |
0 | . | 0 | 7 | |
0 | . | 0 | 7 | 7 |
Fill in the empty spaces with a zero:
Units | Decimal Point | Tenths | Hundredths | Thousandths |
0 | . | 7 | 0 | 0 |
0 | . | 7 | 7 | 0 |
0 | . | 0 | 7 | 0 |
0 | . | 0 | 7 | 7 |
We can now easily compare the values.
Check you have answered the question
The descending order is:
Write all values in their original form.
The decimals and percentage in descending order are:
Place these in ascending order
Convert all the values into the same form: fractions, decimals or percentages.
Three of the values are percentages and one is a fraction so we can convert the single fraction to a percentage.
With percentages; check they all are out of
As all the percentages are shown with the
Compare the value before the % sign.
Because each percentage is out of
We can see that
Check you have answered the question
The ascending order is
Write all values in their original form.
The ascending order is:
Place these in ascending order:
Convert all the values into the same form: fractions, decimals or percentages.Β
The three values given are in different forms, you therefore need to write them in the same form. In this example we will use decimals as the common form but you could use fractions or percentages.
Let’s convert each value to a decimal
Write each out value
So the three values as decimals form are:
Check you have answered the question
The values in ascending order are:
Write all values in their original form.
The values in ascending order are:
Extra: try this questions again using fraction or percentages as your common form.
Place these in ascending order:
Convert all the values into the same form: fractions, decimals or percentages.
The three values given are in different forms, you therefore need to write them in the same form. In this example we will use percentages as the common form but you could use decimals or fractions.
With percentages; check they all are out of
As all the percentages are shown with the
Compare the value before the % sign.
Because each percentage is out of
We can see that
Check you have answered the question e.g. are they in ascending order?
The ascending order is:
Write all values in their original form.
The ascending order is:
Extra: try this questions again using decimals or fractions as your common form
Incorrect conversion between fractions, decimals and percentages will result in the incorrect answer.
Not taking place value into account when comparing decimals will result in the incorrect answer.
E.g.
Not finding a common denominator when comparing and ordering fractions will result in the incorrect answer .
A common error is to confuse ascending and descending.
1. Which of the below is not equivalent to 50\%?
\frac{5}{100} as a percentage is 5\% because \% means out of 100 .
Therefore \frac{5}{100} β 50\%
2. Which of the below is not equivalent to \frac{1}{4}?
4\% is equal to \frac{4}{100} which when simplified is \frac{1}{25} β \frac{1}{4}
3. Which of the below is not equivalent to 0.2?
2 \%=\frac{2}{100}=0.02 β 0.2
4. Which value below is greater than Β \frac{2}{3}?
70 \%=\frac{70}{100}=\frac{7}{10}=\frac{21}{30}
\frac{2}{3}=\frac{20}{30}
Therefore, \quad \frac{21}{30}>\frac{20}{30}
Therefore, \quad \frac{7}{10}>\frac{2}{3}
Therefore, \quadΒ 70 \%>\frac{2}{3}
5. Place these in ascending order Β 0.3,Β 32\%,Β \frac{31}{100}
So the numbers in ascending order are Β 0.3, \frac{31}{100},Β 32 \%Β
6. Place these in descending order \frac{8}{9},Β 90 \%,Β 0.89
They are equivalent
So the numbers in descending order are 90\%,Β 0.89, \frac{8}{9}Β
1.Β Write these numbers in ascending order:
0.82, \quad \frac{4}{5}, \quad 85 \%, \quad \frac{2}{3}, \quad \frac{7}{8}
(3 marks)
Attempt to convert all values to the same formatΒ with at least one conversion correct carried out.
(1)
Smallest and largest values:
\frac{2}{3} – smallest
\frac{7}{8} – largest
(1)
Correct order with all given in original form:
\frac{2}{3}, \quad \frac{4}{5}, \quad 0.82,Β \quad 85 \%,Β \quad \frac{7}{8}
(1)
2. Write these numbers in ascending order:
70 \%, \quad \frac{3}{4},\quad 0.6, \quad \frac{2}{3}
(3 marks)
Attempt to convert all values to the same formatΒ with at least one conversion correct carried out.
(1)
Smallest and largest values:
0.6 – smallest
\frac{3}{4} – largest
(1)
Correct order with all given in original form:
0.6, \quad \frac{2}{3}, \quad 70 \%, \quad \frac{3}{4}
(1)
3. Write these numbers in ascending order:
0.4, \quad \frac{7}{15},\quad 35 \%, \quad \frac{3}{7}
(3 marks)
Attempt to convert all values to the same formatΒ with at least one conversion correct carried out.
(1)
Smallest and largest values:
35 \% – smallest
\frac{7}{15} – largest
(1)
Correct order with all given in original form:
35 \%, \quad 0.4, \quad \frac{3}{7}, \quad
\frac{7}{15}
(1)
4. Β Jamaal received his scores for his recent tests:
–Β Art \quad \quad \quad \quad \quad \quad \quad \frac{14}{25}
–Β Biology \;\quad \quad \quad \quad \quad 64 \%
–Β German \quad \quad \quad \quad \quad\; 49 \%
–Β Sports Science \quad \quad \quad \frac{25}{43}
–Β Music \quad \quad \quad \quadΒ \quad \quad \frac{11}{15}
–Β PhysicsΒ \quad \quad \quad \quad \quad\; 54 \%
Arrange the subjects in order starting with the highest test score.
(3 marks)
Attempt to convert all values to the same format.Β with at least one conversion correct carried out
(1)
Smallest and largest values:
German 49 \% – smallest
Art \frac{14}{25} – largest
(1)
Correct order with all given (listed by subject):
Music, Biology, Sports Science, Art, Physics, German.
(1)
You have now learned how to:
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