Lesson 3: 6-3 Represent Percents Greater Than 100 or Less Than 1

Property

To convert a percent greater than 100 to a fraction, write the percent value as the numerator over a denominator of 100 and simplify. To convert the percent to a decimal, divide by 100 (or move the decimal point two places to the left).

Examples

• To convert $175\%$ to a fraction and decimal:

Fraction: $175\% = \frac{175}{100} = \frac{7}{4} = 1\frac{3}{4}$
Decimal: $175\% = 1.75$

• To convert $350\%$ to a fraction and decimal:

Fraction: $350\% = \frac{350}{100} = \frac{7}{2} = 3\frac{1}{2}$
Decimal: $350\% = 3.5$

Explanation

A percent greater than 100 represents a value larger than one whole. When converting such a percent, the resulting fraction will be an improper fraction or mixed number greater than 1. Similarly, the decimal equivalent will be a number greater than 1. The fundamental process of dividing the percent value by 100 remains the same for any percent.

Property

To convert a fractional percent to a fraction, divide the fraction by 100. To convert to a decimal, first write the fractional percent as a decimal percent, then divide by 100 (move the decimal point two places to the left).

Examples

• Convert $\frac{1}{4}\%$ to a fraction and a decimal.

Fraction: $\frac{1}{4}\% = \frac{1}{4} \div 100 = \frac{1}{4} \times \frac{1}{100} = \frac{1}{400}$
Decimal: $\frac{1}{4}\% = 0.25\% = 0.0025$

• Convert $\frac{2}{5}\%$ to a fraction and a decimal.

Fraction: $\frac{2}{5}\% = \frac{2}{5} \div 100 = \frac{2}{5} \times \frac{1}{100} = \frac{2}{500} = \frac{1}{250}$
Decimal: $\frac{2}{5}\% = 0.4\% = 0.004$

Explanation

A fractional percent is a percent that is less than 1, such as $\frac{1}{2}\%$. To convert any percent to a fraction or decimal, you must divide by 100. For a fractional percent, this means dividing the fraction by 100, which is the same as multiplying by $\frac{1}{100}$. To convert to a decimal, it is often easiest to write the fraction as a decimal first, and then move the decimal point two places to the left.

Property

To convert a decimal percent to a decimal or fraction, divide the percent value by 100. For a decimal percent $d\%$, the equivalent decimal or fraction is $\frac{d}{100}$.

Examples

• Convert $0.5\%$ to a fraction and a decimal.

Decimal: $0.5 \div 100 = 0.005$
Fraction: $\frac{0.5}{100} = \frac{5}{1000} = \frac{1}{200}$

• Convert $0.25\%$ to a fraction and a decimal.

Decimal: $0.25 \div 100 = 0.0025$
Fraction: $\frac{0.25}{100} = \frac{25}{10000} = \frac{1}{400}$

Explanation

A decimal percent less than 1, such as $0.5\%$, represents a very small part of a whole. To convert it to a decimal, divide by 100, which is the same as moving the decimal point two places to the left. To write it as a fraction, place the decimal percent value over 100, then multiply the numerator and denominator by a power of 10 to eliminate the decimal and simplify.