Relate fractions, decimals, and percents

A fraction, decimal, and percent can represent the same rational quantity in different forms: fractions compare a part to a whole, decimals express the quantity through place value, and percents express it as a rate per 100. The learner connects these representations using equivalent fractions, division, multiplication or division by 100, and number-line or hundred-grid models, recognizing that percent is not a separate kind of quantity; the focus is on common terminating decimal and percent cases rather than repeating decimals or more advanced generalizations.

Detailed Explanation: 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\%}

Learn by doing: Relate fractions, decimals, and percents

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Percents to Fractions - Standard

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