Decimals as fractions

A decimal and a fraction are two ways of writing the same number. Once you see the link, switching between them is easy.

From decimal to fraction

The trick: look at the last digit's place, and use that as the denominator.

0.7 — last digit is in tenths, so the fraction is $\frac{7}{10}$.

0.23 — last digit is in hundredths, so the fraction is $\frac{23}{100}$.

0.05 — last digit is in hundredths, so the fraction is $\frac{5}{100}$.

The numerator is just the digits after the point read as a whole number.

From fraction to decimal — the easy cases

When the fraction has a denominator that is 10, 100 or 1 000, the conversion is almost copy-and-paste:

$\frac{4}{10}$ = 0.4

$\frac{29}{100}$ = 0.29

$\frac{3}{100}$ = 0.03 (note the zero — three is in hundredths, not tenths)

Tip: count the zeros in the denominator. That tells you how many digits must sit after the decimal point.

Equivalent fractions and decimals

The same decimal can match many fractions of equal value.

0.5 = $\frac{5}{10}$ = $\frac{1}{2}$ = $\frac{50}{100}$ = $\frac{500}{1000}$

The number on the number line is the same — you just chose a different denominator to label it.

Simplifying

When the fraction can be simplified, the simpler form is usually nicer:

Learn these three — they show up everywhere (in measures, in money, in fractions of a turn).

Trickier fractions for later

Not every fraction has a clean decimal in tenths or hundredths.

$\frac{1}{3}$ = 0.333… (the threes go on forever)

In Year 4 you don't have to convert these. They wait for Year 5 and beyond.

What's next

• For parents
• Back to the introduction
• Comparing decimals

Try it out

• 🔄 Decimal ↔ fraction — swap between the two forms
• 🔢 Decimal place value