A fraction, a decimal and a percentage can all describe exactly the same amount, just written in a different way. Knowing how to swap between the three forms is one of the most useful skills in maths, from reading a sale sign in a shop to understanding a test result or a weather forecast.
To change a fraction to a decimal, divide the numerator (the top number) by the denominator (the bottom number). To change a decimal to a percentage, multiply by 100, since "percentage" simply means "out of 100". To go the other way, from a percentage back to a fraction, write the percentage over 100 and simplify if you can. Fraction, decimal and percentage are just three different ways of writing the exact same amount.
3/4 as a decimal: 3 ÷ 4 = 0.75
0.75 as a percentage: 0.75 × 100 = 75%
So 3/4 = 0.75 = 75%
Complete the missing fraction, decimal or percentage in each row of the table. Use what you learnt about converting between the three forms.
| Row | Fraction | Decimal | Percentage |
|---|---|---|---|
| 1 | 1/2 | ||
| 2 | 0.25 | ||
| 3 | 10% | ||
| 4 | 3/5 | ||
| 5 | 0.75 | ||
| 6 | 20% |
Finding a percentage of an amount means working out that fraction of a quantity, such as money, a length or a group of people. You use this in real life to work out a sale discount, a tip, or how many students in a class chose a particular answer. The easiest way to start is by finding 10% of the amount, because 10% is always the amount divided by 10, which is the same as moving the decimal point one place to the left.
Once you know 10%, you can build up to almost any percentage. For 20%, double the 10% amount. For 5%, halve the 10% amount. For 1%, divide the whole amount by 100. For 50%, simply halve the whole amount. Once you have these "friendly" percentages worked out, add or multiply them together to find trickier percentages, like 30% or 45%.
Find 30% of $40.
Step 1: find 10% of $40 by dividing by 10. 10% of $40 = $4.
Step 2: 30% is 3 lots of 10%, so multiply. 3 × $4 = $12.
So 30% of $40 = $12.
Shade each hundredths grid to match the percentage given. Each grid has 100 small squares, so every square is worth 1%.
Look carefully at each question below. You may convert the numbers to a common form on scrap paper before you answer.
Write these six numbers in order from smallest to largest: 3/10, 45%, 0.6, 1/4, 80%, 0.05
Decide if each statement is true or false.
Which of these numbers is the largest?
Solve each problem. Show your working in the space given, and write full sentence answers for the word problems.
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