A fraction, a decimal and a percent can all describe the same amount. Which one to use is a question of convenience. Converting between them is a small set of moves, and they are worth practising until none of them requires thought.
The conversions
| From | To | What to do | Example |
|---|---|---|---|
| Fraction | Decimal | Divide the top by the bottom | 3/4 = 3 / 4 = 0.75 |
| Decimal | Percent | Multiply by 100, add the sign | 0.75 = 75 percent |
| Percent | Decimal | Divide by 100 | 45 percent = 0.45 |
| Decimal | Fraction | Write over 10, 100 or 1,000, then simplify | 0.6 = 6/10 = 3/5 |
| Fraction | Percent | Convert to a decimal first | 1/8 = 0.125 = 12.5 percent |
| Percent | Fraction | Write over 100 and simplify | 40 percent = 40/100 = 2/5 |
Worth memorising
| Fraction | Decimal | Percent |
|---|---|---|
| 1/2 | 0.5 | 50 percent |
| 1/4 | 0.25 | 25 percent |
| 3/4 | 0.75 | 75 percent |
| 1/5 | 0.2 | 20 percent |
| 1/3 | 0.333 repeating | 33.3 percent, about |
| 1/8 | 0.125 | 12.5 percent |
| 1/10 | 0.1 | 10 percent |
Repeating decimals
Dividing 1 by 3 never terminates. The digits repeat forever, written 0.333... or with a bar over the repeating digit. This is not an approximation problem to be fixed. It is what one third looks like in base ten, and it is why fractions remain the exact form.
Why the division never ends
1 / 3 3 into 10 goes 3 times, remainder 1 3 into 10 goes 3 times, remainder 1 3 into 10 goes 3 times, remainder 1 the same remainder returns, so the digits repeat
Common mistakes
Moving the point the wrong way
Percent means per hundred, so a percent is always the larger looking number. 0.45 is 45 percent, not 0.45 percent, which would be a very small amount.
Dividing the wrong way round
3/4 means three divided by four, giving 0.75. Four divided by three gives 1.333..., which is a different number.
Check yourself
Write 7/8 as a decimal and a percent.
7 / 8 = 0.875, which is 87.5 percent.
Write 0.24 as a fraction in lowest terms.
24/100, and dividing top and bottom by 4 gives 6/25.
Write 150 percent as a decimal and a fraction.
1.5 and 3/2. A percent above one hundred is simply more than one whole.
Which is larger, 2/5 or 45 percent?
45 percent. 2/5 is 0.4, which is 40 percent.
See also
Sources
- Standard conversions among fractions, decimals and percents in United States upper elementary mathematics. Examples on this page are our own.