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Decimals as fractions

Fractions, grade 6 Lesson 14 of 22Learning

Decimals as fractions

You already know decimals – and they are really fractions: 0.6=610\displaystyle {0.6}={\frac{6}{10}}, 0.25=25100\displaystyle {0.25}={\frac{25}{100}}.

From a fraction to a decimal
13\displaystyle \frac{1}{3}, for one, cannot be expanded like this.

A decimal is a fraction whose denominator is 10, 100, 1000 … – so to write a fraction as a decimal, expand it to such a denominator:

35=610=0.614=25100=0.2538=3751000=0.375\displaystyle {\frac{3}{5}}={\frac{6}{10}}={0.6 \qquad \frac{1}{4}}={\frac{25}{100}}={0.25 \qquad \frac{3}{8}}={\frac{375}{1000}}={0.375}

Exercise 1

Expand to the denominator 10, 100 or 1000, and write as a decimal.

a

    / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

    / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

    b

      / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

      / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

      c

        / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

        / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

        From a decimal to a fraction

        And the other way: write the decimal as a fraction whose denominator is 10, 100 or 1000, and reduce:

        0.8=810=450.35=35100=7201.25=125100=114\displaystyle {0.8}={\frac{8}{10}}={\frac{4}{5} \qquad 0.35}={\frac{35}{100}}={\frac{7}{20} \qquad 1.25}={1\frac{25}{100}}={1\frac{1}{4}}

        Exercise 2

        Write as a fraction in its simplest form (or as a mixed number).

        a

          / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

          / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

          b

            / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

            / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

            c

              / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

              / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power