Express each of the following as a percent.
a. 0.032
b. 0.2
c. [tex]$\frac{3}{20}$[/tex]
d. [tex]$\frac{13}{8}$[/tex]
e. [tex]$\frac{1}{6}$[/tex]
f. [tex]$\frac{1}{40}$[/tex]
Answer (2)
To express a decimal as a percent, multiply by 100.
To express a fraction as a percent, convert it to a decimal and then multiply by 100.
0.032 becomes 0.032 × 100 = 3.2% .
The final answers are: 3.2%, 20%, 15%, 162.5%, 16 3 2 % ≈ 16.67% , and 2.5%. 3.2% , 20% , 15% , 162.5% , 16.67% , 2.5%
Explanation
Understanding the Problem We need to convert the given decimals and fractions into percentages. To convert a decimal to a percentage, we multiply it by 100. To convert a fraction to a percentage, we can first convert it to a decimal by dividing the numerator by the denominator, and then multiply by 100.
Converting 0.032 to a Percentage a. To convert 0.032 to a percentage, we multiply it by 100: 0.032 × 100 = 3.2% .
Converting 0.2 to a Percentage b. To convert 0.2 to a percentage, we multiply it by 100: 0.2 × 100 = 20% .
Converting 3/20 to a Percentage c. To convert 20 3 to a percentage, we first convert it to a decimal: 20 3 = 0.15 . Then, we multiply by 100: 0.15 × 100 = 15% .
Converting 13/8 to a Percentage d. To convert 8 13 to a percentage, we first convert it to a decimal: 8 13 = 1.625 . Then, we multiply by 100: 1.625 × 100 = 162.5% .
Converting 1/6 to a Percentage e. To convert 6 1 to a percentage, we first convert it to a decimal: 6 1 = 0.1666 … . Then, we multiply by 100: 0.1666 ⋯ × 100 = 16.66 … % = 16 3 2 % ≈ 16.67% .
Converting 1/40 to a Percentage f. To convert 40 1 to a percentage, we first convert it to a decimal: 40 1 = 0.025 . Then, we multiply by 100: 0.025 × 100 = 2.5% .
Final Answer Therefore, the percentages are: a. 3.2% b. 20% c. 15% d. 162.5% e. 16 3 2 % ≈ 16.67% f. 2.5%
Examples
Percentages are used everywhere in daily life, from calculating discounts while shopping to understanding statistics in news reports. For example, if a store offers a 20% discount on an item, you can calculate the discounted price by converting 20% to a decimal (0.20) and multiplying it by the original price. Understanding percentages helps you make informed decisions and compare different options effectively.
To express the given decimals and fractions as percentages, multiply by 100 or convert fractions to decimals first then multiply. This gives you the following results: 3.2%, 20%, 15%, 162.5%, 16.67%, and 2.5%. Each conversion follows a simple multiplication or decimal conversion process.
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