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Fractions, decimals and percents

Percent, ratio and scale, grade 6 Lesson 2 of 11Learning

Fractions, decimals and percents

A percent is a hundredth, so every fraction and every decimal can be written as a percent: write it as a fraction whose denominator is 100.

Expanding to the denominator 100

Expand the fraction to the denominator 100, and the numerator is the number of percent:

35=60100=60%720=35100=35%950=18100=18%\displaystyle {\frac{3}{5}}={\frac{60}{100}}={60\% \qquad \frac{7}{20}}={\frac{35}{100}}={35\% \qquad \frac{9}{50}}={\frac{18}{100}}={18\%}

A decimal is written in hundredths first:

0.4=40100=40%0.05=5100=5%\displaystyle {0.4}={\frac{40}{100}}={40\% \qquad 0.05}={\frac{5}{100}}={5\%}

Exercise 1

Write as a percent.

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

        d
        Here you reduce, not expand.

          / – 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

          To a percent by division
          13=0.333…\displaystyle {\frac{1}{3}}={0.333\ldots} – that is, 3313%\displaystyle 33\frac{1}{3}\%.

          38\displaystyle \frac{3}{8} cannot be expanded to the denominator 100: 100 is not divisible by 8.
          Then divide the numerator by the denominator, and you get a decimal: 38=3÷8=0.375\displaystyle {\frac{3}{8}}={3\div8}={0.375}.
          0.375 is 37.5 hundredths, that is, 37.5%\displaystyle 37.5\%.

          Percents to know by heart
          1212%\displaystyle 12\frac{1}{2}\% is half of 25%\displaystyle 25\%, as 18\displaystyle \frac{1}{8} is half of 14\displaystyle \frac{1}{4}.

          These percents are worth knowing by heart – with them you calculate in your head:

          • 50%=12\displaystyle {50\%}={\frac{1}{2}}
          • 25%=14\displaystyle {25\%}={\frac{1}{4}}
          • 75%=34\displaystyle {75\%}={\frac{3}{4}}
          • 10%=110\displaystyle {10\%}={\frac{1}{10}}
          • 20%=15\displaystyle {20\%}={\frac{1}{5}}
          • 1212%=18\displaystyle {12\frac{1}{2}\%}={\frac{1}{8}}
          Exercise 2

          Write the fraction as a percent, and the percent as a fraction in its simplest form.

          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

                Comparing fractions, decimals and percents

                To compare a fraction, a decimal and a percent, write them all the same way – as percents, for one.
                Which number is the greatest: 25\displaystyle \frac{2}{5}, 0.35\displaystyle 0.35 or 38%\displaystyle 38\%?
                25=40%\displaystyle {\frac{2}{5}}={40\%} and 0.35=35%\displaystyle {0.35}={35\%}, so 0.35<38%<25\displaystyle 0.35<38\%<\frac{2}{5}.

                Exercise 3

                Put in order from the smallest to the greatest:

                340.772%450.08\displaystyle \frac{3}{4} \qquad 0.7 \qquad 72\% \qquad \frac{4}{5} \qquad 0.08