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Singapore Primary Maths

Primary 5 Foundation maths · Decimals · About 12 minutes

Express decimals as fractions

Keep the chosen amount unchanged while naming its place-value units.

Start the interactive lesson →Open practice activity

What you will learn

Models used: number sentences, stories, diagrams.

Before you start

Read the last decimal place to name the fraction

How can we write 0.35 as a fraction?

  1. Read the place heading before the digit. A counter in a different column has a different value.

    The last digit is in the hundredths column. So 0.35 means thirty-five hundredths.

    0.35 = 35/100

    0.35 = 3 tenths + 5 hundredths

  2. The whole grid has 100 equal squares. One full row is 10 hundredths, or one tenth.

    Shade 35 squares of a hundred-square whole. This shows why the denominator is one hundred.

    35 shaded parts out of 100

    One small square is one hundredth of the whole. Ten small squares make one tenth, so the same shaded amount can be described in more than one way.

    35/100 = 0.35 = 35%

  3. The complete bar is the whole. Each labelled section is one part of it.

    If we simplify, divide both numbers by five. Seven groups of five shaded squares are out of twenty groups of five.

    35/100 = 7/20

  4. The whole grid has 100 equal squares. One full row is 10 hundredths, or one tenth.

    Both fractions describe the same amount. Simplifying changes the size and count of parts together.

    0.35 = 35/100 = 7/20

    One small square is one hundredth of the whole. Ten small squares make one tenth, so the same shaded amount can be described in more than one way.

    35/100 = 0.35 = 35%

What did the picture help us see?

Both fractions describe the same amount. Simplifying changes the size and count of parts together.

Worked example: A new example, together

Write 0.62 as a fraction in simplest form.

0.62 = 6 tenths + 2 hundredths

  1. Read the place heading before the digit. A counter in a different column has a different value.

    Keep the chosen amount unchanged while naming its place-value units.

    Each decimal column names a unit ten times smaller than the one before it. Matching those units keeps the value clear.

  2. Read the place heading before the digit. A counter in a different column has a different value.

    The fraction means 62 ÷ 100.

    Write 0.62 as a fraction in simplest form.

    31/50

  3. Read the place heading before the digit. A counter in a different column has a different value.

    Rename it in hundredths: 62/100.

    0.62 = 6 tenths + 2 hundredths

  4. Read the place heading before the digit. A counter in a different column has a different value.

    62/100 = 0.62.

    0.62 = 6 tenths + 2 hundredths

  5. Read the place heading before the digit. A counter in a different column has a different value.

    Check the result against the question we started with.

    Undo the operation to recover the starting quantity.

    We found 31/50. Each decimal column names a unit ten times smaller than the one before it. Matching those units keeps the value clear.

    0.62 = 6 tenths + 2 hundredths

Common mistakes to discuss

Check your understanding

Explain your reasoning to an adult, then try a fresh question in the interactive lesson. A result from one attempt is not proof of lasting mastery.

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