Converting between fractions, decimals and percentages - AQAConverting decimals to fractions and percentages
Fractions, decimals and percentages are frequently used in everyday life. Knowing how to convert between them improves general number work and problem solving skills.
To convert a decimalA number that uses powers of 10 as place value. In the example of 0.82, the 8 represents tenths and the 2 represents hundredths. to a fractionA fraction is a part of a whole, for example 1/2., use place value. The first number after the decimal place is worth tenths, the next is worth hundredths, the next thousandths and so on.
Example
What is 0.7 as a fraction?
Hundreds
Tens
Units
.
Tenths
Hundredths
Thousandths
0
.
7
Hundreds
Tens
Units
0
.
.
Tenths
7
Hundredths
Thousandths
The 7 represents tenths, so this can be written as \(\frac{7}{10}\). This fraction cannot be simplifyA fraction is simplified when there are no more common factors shared by the numerator and denominator. For example, the fraction 8/10 simplifies to 4/5 by dividing the numerator and denominator by the common factor of 2. or cancelled down so it is the final answer.
Question
What is 0.46 as a fraction?
Hundreds
Tens
Units
.
Tenths
Hundredths
Thousandths
0
.
4
6
Hundreds
Tens
Units
0
.
.
Tenths
4
Hundredths
6
Thousandths
0.46 is worth 46 hundredths which is written as \(\frac{46}{100}\). 2 is a common factor of 46 and 100, so \(\frac{46}{100}\) simplifies to \(\frac{23}{50}\).
0.46 is \(\frac{23}{50}\) as a fraction.
Converting decimals to percentages
Once a number is written as a decimal, it can be converted to a percentageA proportion representing parts per hundred, for example 9% is 9 out of 100, or 9/100.. Remember that 'per cent' means 'per hundred', so converting from a decimal to a percentage can be done by multiplying by 100 (move the digits two places to the left).
0.375 as a percentage = \(0.375 \times 100 = 37.5 \%\)