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Percentages as fractions and decimals

Percentages as fractions and decimals

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Tutor: Labib

Summary

Percentages as fractions and decimals 

​​​​In a nutshell

Percentages, decimals and fractions are all different ways of expressing quantities or proportions. Being able to convert between the different forms is a very important skill to have. There are also some "common" conversions which you should aim to learn off by heart.



Equivalence

Definition

Equivalent means equal in value.  If a percentage, decimal or fraction is equivalent to one another, this means they represent the same value.



Halves, quarters and fifths

These fractions feature often in maths problems, so it is helpful to try to learn their equivalent values off by heart.


Percentage

Fraction

Decimal

50%50\%​​
12\frac{1}{2}​​
0.50.5​​
25%25\%​​
14\frac{1}{4}​​
0.250.25​​
75%75\%​​
34\frac{3}{4}​​
0.750.75​​
20%20\%​​
15\frac{1}{5}​​
0.20.2​​
40%40\%​​
25\frac{2}{5}​​
0.40.4​​
60%60\%​​
35\frac{3}{5}​​
0.60.6​​
80%80 \%​​
45\dfrac{4}{5}​​
0.80.8​​


Example 1

What is 35\dfrac{3}{5} as a percentage?


Find 35\dfrac{3}{5} in the table above. Read along to the percentage column and give the equivalent value.

35=60%\dfrac{3}{5} = \underline{60\%}​​


Example 2

What is 75%75\% as a fraction?


Find 75%75\% in the table above. Read along to the fraction column and give the equivalent value.

75%=3475\%=\underline {\dfrac{3}{4}}​​


Tip: The more you practise with your equivalent values, the easier they become to remember!



Tenths and twenty-fifths

The table below shows the equivalent values of one tenth and one twenty-fifth.


PERCENTAGE
FRACTION
DECIMAL
10%10\%​​
110\dfrac{1}{10}​​
0.10.1​​
4%4\%​​
125\frac{1}{25}​​
0.040.04​​


You can use these values, along with multiplication to figure out more complicated conversions.


Example 3

What is 30%30\% as a fraction?


Recall that 10%=11010\% = \dfrac{1}{10}.


Calculate the multiplier to reach 30%30\%.

10%×3=30%10 \% \times 3 = 30\%​​


Multiply the equivalent fraction by the multiplier.

110×3=310\dfrac{1}{10} \times 3=\underline{\dfrac{3}{10}}​​



Example 4

What is 16%16 \% as a decimal?


Recall that 4%=0.044\%= 0.04.


Calculate the multiplier to reach 16%16\%.

4%×4=16%4\%\times 4 = 16\%​​


Multiply the equivalent decimal by the multiplier.

0.04×4=0.160.04 \times 4 = \underline{0.16}​​


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Exercises

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FAQs - Frequently Asked Questions

Which conversions should I know off by heart?

What does equivalent mean?

How are percentages, fractions and decimals related?

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