Topic 3 of 12

Decimals and percents

Step 8 · Ratios and negative numbers topics

Fractions, decimals and percents are three ways to write the same number. Learn to move between them, find a percent of an amount, and multiply and divide decimals.

Percent means per hundred

Percent means out of 100. So 35% is 35 out of 100, which is the fraction $\frac{35}{100}$ and the decimal 0.35. Some pairs are worth knowing by heart:

Fraction	Decimal	Percent
$\frac{1}{2}$	0.5	50%
$\frac{1}{4}$	0.25	25%
$\frac{3}{4}$	0.75	75%
$\frac{1}{5}$	0.2	20%
$\frac{1}{10}$	0.1	10%

Changing between the three

Fraction to decimal: divide the top by the bottom. $\frac{3}{8} = 3 \div 8 = 0.375$ .
Decimal to percent: multiply by 100, which moves the decimal point two places to the right. $0.375 = 37.5\%$ .
Percent to decimal: divide by 100, which moves the decimal point two places to the left. $6\% = 0.06$ .
Percent to fraction: write it over 100 and simplify. $45\% = \frac{45}{100} = \frac{9}{20}$ .

Finding a percent of an amount

To find a percent of an amount, change the percent to a decimal and multiply.

Example: Percent of a number

Find 30% of 80.

Change the percent to a decimal: $30\% = 0.30$ .
Multiply: $0.30 \times 80 = 24$ .

Answer24

Example: A discount

A $45 jacket is 20% off. What is the sale price?

Find the discount: $0.20 \times 45 = 9$ , so $9 off.
Subtract it from the price: $45 - 9 = 36$ .

Answer$36

Finding the whole

Sometimes you know the part and the percent, and need the whole amount. Divide the part by the percent written as a decimal.

Example: Part and percent known

15 students are 25% of a class. How many students are in the class?

Write what you know: 25% of the class is 15, so $0.25 \times \text{class} = 15$ .
Divide the part by the decimal: $15 \div 0.25 = 60$ .
Check: 25% of 60 is $0.25 \times 60 = 15$ .

Answer60 students

Multiplying and dividing decimals

To multiply decimals, multiply as if there were no decimal points. Then count the decimal places in both numbers together and give the answer that many. For $0.3 \times 0.25$ : $3 \times 25 = 75$ , and the two numbers have three decimal places between them, so the answer is 0.075.

To divide by a decimal, move the decimal point in both numbers the same number of places to the right until the number you are dividing by is whole. For $4.5 \div 0.15$ , move both points two places: $450 \div 15 = 30$ .

Try it yourself

Work each one on paper first, then open the answer to check.

Write $\frac{3}{5}$ as a decimal and as a percent.
Show answer
0.6 and 60%. $3 \div 5 = 0.6$ , and $0.6 \times 100 = 60$ .
Write 8% as a decimal and as a fraction in simplest form.
Show answer
0.08 and $\frac{2}{25}$ . $\frac{8}{100}$ simplifies by dividing top and bottom by 4.
Find 15% of 60.
Show answer
9, because $0.15 \times 60 = 9$ .
A game costs $40 and is 25% off. What is the sale price?
Show answer
$30. The discount is $0.25 \times 40 = 10$ , and $40 - 10 = 30$ .
$0.6 \times 0.25$
Show answer
0.15, because $6 \times 25 = 150$ , and three decimal places gives 0.150, which is 0.15.
18 is 30% of what number?
Show answer
60, because $18 \div 0.30 = 60$ .