Foundation and Higher · fraction to decimal

Fractions to decimals
and back again.

a fraction is
just a division

the line in a fraction means —

÷

38 is 3 ÷ 8

every fraction is a division

step 1 of 4

Fraction to decimal

1. Divide the top by the bottom.

2. Use short division, or a calculator.

✓ Learn: 18 = 0.125, so 38 = 0.375

38

= 3 ÷ 8 top ÷ bottom

= 0.375

step 2 of 4

Decimal to fraction

1. Two decimal places: write it over 100.

2. Simplify: divide top and bottom by 5.

✓ One place over 10, three over 1000

0.35

= 35100two decimal places: hundredths

= 720÷ 5

step 3 of 4

Recurring decimals

1. A dot shows the digit that repeats.

2. Two dots: all between them repeats.

✓ Only dot the part that repeats

13 = 0.333… = 0.3

211 = 0.1818… = 0.18

16 = 0.1666… = 0.16

step 4 of 4

Which ones end?

1. 8, 20, 25 are built from 2s and 5s.

2. 3, 6, 11 have other prime factors.

✓ 2s and 5s only: the decimal ends

38720925 terminate

1356211 recur

only 2s and 5s in the denominator

fractions and decimals —

Fraction to decimal

top ÷ bottom

Decimal to fraction

over 10, 100 or 1000, simplify

Recurring

dots over what repeats

Simplify the fraction first
before checking the denominator.

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