Lesson 2: Comparing and Ordering Fractions, Decimals, and Percents

Property

To convert a percent to a fraction, use the definition: $25\% = \frac{25}{100}$. To convert a percent to a decimal, drop the % symbol and move the number’s decimal point two places to the left. To convert a decimal to a percent, move the decimal point two places to the right and writing the % symbol on the right side. To convert a fraction to a percent, create an equivalent fraction with a denominator of 100, like $\frac{2}{5} = \frac{2 \times 20}{5 \times 20} = \frac{40}{100} = 40\%$.

Examples

• To convert 60% to a fraction, write it as $\frac{60}{100}$ and simplify to $\frac{3}{5}$.

• To convert the decimal $0.85$ to a percent, move the decimal two places to the right to get 85%.

Property

Since fractions, decimals, and percents can all be rewritten in any of these three forms, we can convert different numerical representations into a uniform format to make comparisons straightforward. Converting to a common form (such as decimals or percentages) allows us to easily determine which number is larger or to place them in order from least to greatest.

Examples

Property

A number line provides a visual representation for comparing fractions, decimals, and percents. Numbers are positioned from left to right in increasing order, with smaller values to the left and larger values to the right. To place fractions, decimals, and percents on a number line, convert them to the same form or use their decimal equivalents to determine their relative positions.

Examples