math · 24 minutes · Official OETT Aligned
Fractions & Decimals
Change from one form to the other
What to know
- dividing top by bottom
- place value
- simplifying a fraction
- common eighths and sixteenths
Measurements often use fractions on a ruler and decimals in a calculation.
The core rule
Fraction to decimal: divide top by bottom. Decimal to fraction: use 10, 100, 1000, and so on, then simplify.
For 3/8, divide 3 by 8 to get 0.375. For 0.625, there are three decimal places, so write 625/1000. Divide both numbers by 125 to get 5/8. Simplifying changes how a fraction looks, not its value.
Worked examples
Example 1: easy
3/8 = 0.375.
- Read 3/8 as the division 3 ÷ 8.
- Long division or an exact benchmark gives 0.375.
A fraction means top number divided by bottom number.
Example 2: medium
0.625 = 5/8.
- Write 0.625 as 625/1000 because it has three decimal places.
- Divide both numbers by 125 to obtain 5/8.
Three decimal places means thousandths.
Example 3: hard
0.4375 = 7/16.
- Write 0.4375 as 4375/10000.
- Divide top and bottom numbers by 625 to reduce the fraction to 7/16.
Write the exact fraction first, then simplify.
Common mistakes
Put every decimal over 10.
Count the decimal places. Use 10 for one place, 100 for two, 1000 for three, and so on.
Put it into practice
Use guided explanations, check your answers, and try a new variation.