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Percent

Percent, ratio and scale, grade 6 Lesson 1 of 11Learning

Percent

A square of 100 squares

This square has 100 equal squares in it, and 25 of them are shaded:

25 squares out of 100 are 25100\displaystyle \frac{25}{100} of the square. In percent: 25 percent of the square is shaded.

A percent is a hundredth

A percent is a hundredth – one part out of 100 equal parts. Its sign is %, so 25 percent is 25%:

a%\displaystyle a\% =\displaystyle = a100\displaystyle \frac{a}{100}
  • 1%=1100\displaystyle {1\%}={\frac{1}{100}} – one square out of 100.
  • 25%=25100\displaystyle {25\%}={\frac{25}{100}} – 25 squares out of 100.
100% and 50%

100%=100100=1\displaystyle {100\%}={\frac{100}{100}}={1} – the whole: all 100 squares.
50%=50100=12\displaystyle {50\%}={\frac{50}{100}}={\frac{1}{2}} – a half:

50 squares out of 100 are half the square.

A percent as a decimal

Hundredths can be written as a decimal too, so every percent is also a decimal:

25%=25100=0.257%=7100=0.07100%=1\displaystyle {25\%}={\frac{25}{100}}={0.25 \qquad 7\%}={\frac{7}{100}}={0.07 \qquad 100\%}={1}

Exercise 1

What percent of the square is shaded?

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

        Exercise 2

        Write 37% as a fraction and as a decimal.

        a
        As a fraction

          / – 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
          As a decimal

            / – 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

            Exercise 3

            Draw a square of 10 by 10 squares.
            Shade 30% of it.