Skill: Relate fractions, decimals, and percents

A fraction, decimal, and percent can show the same amount in different ways:

• A fraction compares a part to a whole.
• A decimal uses place value.
• A percent means “out of 100.”

Example: Write $\frac{3}{5}$ as a decimal and a percent.

Step 1: Convert the fraction to a decimal.

Divide the numerator by the denominator:

$$3 \div 5 = 0.6$$

So,

$$\frac{3}{5}=0.6$$

Step 2: Convert the decimal to a percent.

A percent is a number out of $100$. Multiply the decimal by $100$, or move the decimal point two places to the right:

$$0.6 \times 100=60$$

Add the percent sign:

$$0.6=60\%$$

Step 3: Check using an equivalent fraction.

Change $\frac{3}{5}$ to a fraction with a denominator of $100$:

$$\frac{3}{5}\times\frac{20}{20}=\frac{60}{100}$$

The fraction $\frac{60}{100}$ means $60$ out of $100$, so it equals $60\%$. It also has the decimal form $0.60$, which is the same as $0.6$.

Therefore,

$$\boxed{\frac{3}{5}=0.6=60\%}$$