Fractions, Decimals and Percentages

Find equivalent representations of rational numbers and represent rational numbers on a number line.

These three are the same idea in three costumes. Being able to swap between them freely is what makes percentage questions easy instead of frightening.

Builds onYr 7 · Equivalent Fractions and Simplifying

Method

Per cent means out of a hundred

35\% = \frac{35}{100}

Every percentage is already a fraction with 100 on the bottom.

Percentage to decimal: divide by 100

35\% = 0{,}35

The point moves two places left.

Decimal to percentage: multiply by 100

0{,}35 = 35\%

The point moves two places right.

Fraction to percentage: make the bottom 100

\frac{3}{4} = \frac{75}{100} = 75\%

Or divide top by bottom, then multiply by 100.

Learn the common ones by heart

\tfrac{1}{2} = 50\% \quad \tfrac{1}{4} = 25\% \quad \tfrac{1}{5} = 20\% \quad \tfrac{1}{3} \approx 33\%

These come up constantly and save time in every other topic.

Worked example

e.g.

\text{Write } \frac{7}{20} \text{ as a decimal and as a percentage.}

Look for a number that turns the bottom into 100. $20 \times 5 = 100$
Multiply the top by the same number. $7 \times 5 = 35$
Write the equivalent fraction. $\frac{7}{20} = \frac{35}{100}$
A fraction over 100 is already a percentage. $\frac{35}{100} = 35\%$
For the decimal, divide the percentage by 100. $35\% = 0{,}35$
Check the three forms agree. $\frac{7}{20} = 0{,}35 = 35\% \quad\checkmark$

Practice

Convert between all three forms.

\text{Write } 0{,}6 \text{ as a percentage.}

Answer

60\%

\text{Write } 45\% \text{ as a decimal.}

Answer

0{,}45

\text{Write } \frac{3}{5} \text{ as a percentage.}

Answer

\frac{60}{100} = 60\%

\text{Write } 8\% \text{ as a fraction in simplest form.}

Answer

\frac{8}{100} = \frac{2}{25}

\text{Write } \frac{5}{8} \text{ as a decimal.}

Answer

5 \div 8 = 0{,}625

\text{Order smallest first: } 0{,}7,\ \tfrac{3}{5},\ 65\%

Answer

\tfrac{3}{5} = 60\%,\ 65\%,\ 0{,}7 = 70\%