To write a percent:

• Write the number in the usual way
• Place the percent sign after the numerals
  • $50\%$
  • $5\frac{1}{2}\%$ or $5.5\%$
  • $\frac{3}{4}\%$ or $0.75\%$

To read a percent:

• Read the numbers in the usual way.
• Say “percent” after the number.
  • $16\%$ — say, “sixteen percent”
  • $4\frac{1}{2}\%$ — say, “four and one-half percent”
  • $0.25\%$ — say, “twenty-five hundredths percent,” or, “one-quarter percent,” or, “point two five percent”

Writing equivalent fractions is an important math skill.

Equivalent common fractions, decimals, and percents all represent the same amount (see Table 5.6.1).

You need the skill of writing equivalent fractions for working with percents.

To change any number to a percent, multiply the number by 100% and place a percent sign % after the product.

Remember this shortcut for multiplying by 100?

$4.27\times100=427$
$0.287\times100=28.7$
$53\times100=5300$

The shortcut is:

When multiplying by 100, move the decimal point two places to the right.

So:

To change a decimal to a percent, move the decimal point two places to the right and then write the percent sign after the number.

If the decimal point moves to the end of the number, it is not necessary to write the decimal point.

Remember: Zeros at the beginning of a number are also not necessary.

$\begin{equation}\begin{split} &\curvearrowright \\ 0.05=0&.05=\cancel{0.0}5\%=5\% \end{split}\end{equation}$

If the decimal is a tenth (one decimal place), it will be necessary to add a zero. If you are changing a whole number to a percent, add two zeros.

$\begin{equation}\begin{split} &\curvearrowright \\ 0.4=0&.40=40\% \end{split}\end{equation}$

$\begin{equation}\begin{split} &\curvearrowright \\ 1.7=1&.70=170\% \end{split}\end{equation}$

$\begin{equation}\begin{split} &\curvearrowright \\ 2=2&.00=200\% \end{split}\end{equation}$

To divide by 100, move the decimal point two places to the left.

So:

To change a percent to a decimal, divide by 100 (move the decimal point two places to the left) and remove the percent sign.

To change a percent containing a common fraction to a decimal:

1. Change the common fraction in the percent to a decimal in the percent.
2. Divide by 100 (move the decimal 2 places to the left).

To change any number to a percent, multiply the number by 100% and place the percent sign % after the product.

There are two methods you can use to change a common fraction to a percent.

Method 1

To change a common fraction to an equivalent percent, multiply the common fraction by 100%.

Method 2

To change a common fraction to an equivalent percent, first write the common fraction as a decimal. Then, multiply the decimal by 100% (move the decimal point two places to the right).

The method you use to change a common fraction to a percent will depend on the numbers you are working with. Choose whichever method seems easier for the situation. You will also memorize many equivalencies as you work with them. But you should definitely memorize:

• $\dfrac{1}{3}=33\dfrac{1}{3}\%$
• $\dfrac{2}{3}=66\dfrac{2}{3}\%$

You know that percents are a form of fraction with an unwritten denominator of 100. A % sign is used.

To change any percent to a decimal, common fraction, or mixed number, divide by 100 and remove the percent sign.

To change a percent to a common fraction:

1. Write the numerals in the percent as the numerator.
2. Write 100 as the denominator.
   • Remember: The line in a fraction can be a division sign, so $58\%=\dfrac{58}{100}$ is the same as $58\div100$.)
3. Remove the % sign.
4. Simplify the fraction: $\dfrac{58}{100}=\dfrac{29}{50}$

Note: Percents greater than or equal to 100 become improper fractions which will be rewritten as mixed numbers.

$110\%=\dfrac{110}{100}=1\dfrac{10}{100}=1\dfrac{1}{10}$

$120\%=\dfrac{120}{100}=1\dfrac{20}{100}=1\dfrac{1}{5}$

Remember: 100% is the whole thing $100\% = 1$.

Sometimes, a percent smaller than 1% is used.

For example, you will hear amounts such as $\tfrac{1}{4}\%$ or $\tfrac{1}{8}\%$ or $\tfrac{1}{2}\%$ on the news about the Bank of Canada rate and the rise and fall of inflation.

These are small amounts. Sometimes, the expression “$\tfrac{1}{2}\text{ of a percentage point}$” is used instead of “$\tfrac{1}{2}\%$”.

What is $\dfrac{1}{4}\%$?

$\dfrac{1}{4}\%$ is $\dfrac{1}{4}\text{ of }1\%$

$1\%=\dfrac{1}{100}$, so $\dfrac{1}{4}\text{ of }1\%=\dfrac{1}{4}\times\dfrac{1}{100}=\dfrac{1}{400}$

$\dfrac{1}{4}\%=0.25\%=0.0025$

What is $\dfrac{1}{2}\%$

$\dfrac{1}{2}\%=\dfrac{1}{2}\text{ of }1\%=\dfrac{1}{2}\times\dfrac{1}{100}=\dfrac{1}{200}$

$\dfrac{1}{2}\%=0.5\%=0.005$

To work with percents less than 1%, change the percent to a decimal by dividing by 100 (move the decimal point two places to the left).

$0.2\%=0.002$

$0.75\%=0.0075$

If the percent is expressed as a common fraction:

• Write the common fraction percent as a decimal percent.
• Divide by 100 (move the decimal point two places left).

These percents will become repeating decimals. For example:

$\begin{equation}\begin{split} 33\dfrac{1}{3}\% &= 33.\overline{3}\% &= 0.33\overline{3} \\ \\ 66\dfrac{2}{3}\% &= 66.\overline{6}\% &= 0.66\overline{6} \end{split}\end{equation}$

It is usually more convenient to use the common fraction equivalent of these percents. Memorize them, or make a note on a special paper and post it near your workspace.

$\begin{equation}\begin{split} 33\dfrac{1}{3}\% &= 33\dfrac{1}{3}\div100 &= \dfrac{100}{3}\times\dfrac{1}{100} \ &= \dfrac{1}{3} \\ \\ 66\dfrac{2}{3}\% &= 66\dfrac{2}{3}\div100 &= \dfrac{200}{3}\times\dfrac{1}{100} \ &= \dfrac{2}{3} \end{split}\end{equation}$

1. Write these percents in numeral form.
   1. Sixty-two and one-half percent
   2. One hundred six and one-fifth percent

    

2. Write these percents in words.
   1. $72\%$
   2. $\dfrac{3}{4}\%$

    

3. Change these percents to decimal fractions.
   1. $32\%$
   2. $18.5\%$
   3. $125\%$
   4. $\dfrac{4}{5}\%$
   5. $\dfrac{2}{3}\%$

    

4. Change these percents to common fractions in the lowest terms.
   1. $16\%$
   2. $20\%$
   3. $106\%$
   4. $75\%$

    

5. Change these common fractions to equivalent percents.
   1. $\dfrac{4}{5}$
   2. $\dfrac{3}{8}$

5.6: Practice Question Answers

1. Write these percents in numeral form.
   1. $62.5\%$ or $62\dfrac{1}{2}\%$
   2. $106.2\%$ or $106\dfrac{1}{5}\%$

    

2. Write these percents in words.
   1. Seventy-two percent
   2. Three-quarters percent

    

3. Change these percents to decimal fractions.
   1. $0.32$
   2. $0.185$
   3. $1.25$
   4. $0.008$
   5. $0.00\overline{6}$

    

4. Change these percents to common fractions in the lowest terms.
   1. $\dfrac{4}{25}$
   2. $\dfrac{1}{5}$
   3. $1\dfrac{3}{50}$
   4. $\dfrac{3}{4}$

    

5. Change these common fractions to equivalent percents.
   1. $80\%$
   2. $37.5\%$

This chapter has been adapted from Topic A: Introducing Percent in Adult Literacy Fundamental Mathematics: Book 6 – 2nd Edition (BCcampus) by Liz Girard and Wendy Tagami (2022), which is under a CC BY 4.0 license.