# Convert between benchmark decimals and fractions

Lesson
##### Setting the benchmark

A benchmark is a reference point against which we can compare or make judgements about numbers. There are a few common fractions and decimals (and percentages) that we use as benchmarks.

The pictures below show these benchmark fractions:

 $0.1$0.1 $0.2$0.2 $0.25$0.25 $0.5$0.5 $0.75$0.75 $10$10 out of $100$100 $20$20 out of $100$100 $25$25 out of $100$100 $50$50 out of $100$100 $75$75 out of  $100$100

In the first grid block, $10$10 out of $100$100 squares are shaded. We could also simplify this and say $1$1 out of the $10$10 columns are shaded, which, if you remember looking at the place value table, is written as $0.1$0.1 as a decimal.

So what about when we see a decimal like $0.5$0.5 written?

Well, just think $0.5$0.5 means $5$5 tenths or $\frac{5}{10}$510 (or $\frac{50}{100}$50100 like is shown in the grid block above), which we can simplify to $\frac{1}{2}$12.

### Summary

Here's a table that summarises these benchmark fractions, decimals and percentages.

Decimal Fraction Fraction in lowest terms Percentage
$0.1$0.1 $\frac{10}{100}$10100 $\frac{1}{10}$110 $10%$10%
$0.2$0.2 $\frac{20}{100}$20100 $\frac{1}{5}$15  $20%$20%
$0.25$0.25 $\frac{25}{100}$25100 $\frac{1}{4}$14 $25%$25%
$0.5$0.5 $\frac{50}{100}$50100 $\frac{1}{2}$12 $50%$50%
$0.75$0.75 $\frac{75}{100}$75100 $\frac{3}{4}$34 $75%$75%

#### Worked Examples

##### QUESTION 1

Write the decimal $0.75$0.75 as a simplified fraction.

##### QUESTION 2

Convert $6.125$6.125 into an improper fraction or mixed number. Give your answer in simplest form.

##### QUESTION 3

Write the decimal $3.8$3.8 as a mixed or improper fraction, giving your answer as a simplified fraction.