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 |
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$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.
Outcomes
NA3-1
Use a range of additive and simple multiplicative strategies with whole numbers, fractions, decimals, and percentages.