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Fractions, decimals and percentages

Fractions, decimals and percentages

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Tutor: Daniel

Summary

Fractions, decimals and percentages

​​In a nutshell

Fractions, decimals and percentages can all be used to represent numbers. Percentages are typically used for comparing one quantity against another, while fractions and decimals are used to represent quantities.



Converting between fractions and decimals

​​Fractions to decimals

To convert from a fraction to a decimal, perform short division by dividing the numerator by the denominator to obtain the decimal form.


Decimals to fractions

​​Procedure

1.
For terminating decimals, multiply the decimal by a number like 1010 or 100100 to make the last digit of the decimal move to the units column. This forms the numerator.
2.
The denominator of the fraction is the number you multiplied by in step 1 (1010 or 100100​ etc).
3.
Simplify the fraction (if required).


Example 1

Convert 1.3751.375​ into a fraction in its simplest form.


1.375×1000=13751.375 \times 1000 = 1375


Hence 1.375=13751000=275200=5540=1181.375 = \dfrac{1375}{1000}=\dfrac{275}{200} =\dfrac{55}{40}= \underline{\dfrac{11}{8}}



Converting between decimals and percentages

Decimals to percentages

To convert from a decimal to a percentage, multiply the decimal by 100100 and put a %\%​ sign at the end of the number.


Percentages to decimals

To convert from a percentage to a decimal, divide the percentage by 100100 and remove the %\%​ sign at the end of the number.



Converting between fractions and percentages

In order to convert between fractions and percentages use the decimal form as an intermediate step.


Example 2

The following are examples of the same number in fraction, decimal and percentage form:


35=0.6=60%\dfrac{3}{5} = 0.6 = 60\%


174=4.25=425%\dfrac{17}{4} = 4.25 = 425\%



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Exercises

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FAQs - Frequently Asked Questions

How do you turn a percentage into a number?

Should percentages have decimals?

How do you change a decimal to a percentage?

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