Question

Write each given percent as a decimal and a fraction in lowest terms Write each given fraction as a decimal and a percent. Social Studies About \(7 \%\) of Americans are under age \(5,\) and about \(13 \%\) are over age 65

Short answer

7% as decimal: 0.07, as fraction: \( \frac{7}{100} \). 13% as decimal: 0.13, as fraction: \( \frac{13}{100} \).

Step-by-step solution

Convert Percent to Decimal

To convert a percent to a decimal, divide by 100. For 7%, \( 7 \div 100 = 0.07 \). For 13%, \( 13 \div 100 = 0.13 \).

Convert Percent to Fraction in Lowest Terms

To convert a percent to a fraction, write the percent as a fraction with 100 as the denominator and then simplify. For 7%, \( \frac{7}{100} \) is already in its lowest terms. For 13%, \( \frac{13}{100} \) is also in its lowest terms.

Sum Up Findings

Summarize the converted values: 7% as a decimal is 0.07 and as a fraction is \( \frac{7}{100} \). 13% as a decimal is 0.13 and as a fraction is \( \frac{13}{100} \).

Key concepts

Percent to Decimal Conversion

Converting a percent to a decimal is a simple process that involves dividing the percent value by 100. This is because 'percent' means per hundred. For example, when you see 7%, it means 7 out of 100. To convert 7% to a decimal, you divide 7 by 100 which gives you 0.07.
Similarly, for 13%, you divide 13 by 100, resulting in 0.13.

• 7% as a decimal: 7 ÷ 100 = 0.07
• 13% as a decimal: 13 ÷ 100 = 0.13

This method works for any percent—just remember to divide by 100!

Percent to Fraction Conversion

To convert a percent to a fraction, you start by writing the percent as a fraction over 100. This is because 'percent' literally means 'per hundred'. Let's take a closer look using our examples:

• 7% becomes \( \frac{7}{100} \).
• 13% becomes \( \frac{13}{100} \).

As shown, both fractions \( \frac{7}{100} \) and \( \frac{13}{100} \) are in their simplest forms since the numerators (7 and 13) do not have any common divisors with the denominator (100) other than 1.

Fraction Simplification

Simplifying fractions means reducing them to their lowest terms by dividing both the numerator (top number) and the denominator (bottom number) by their greatest common divisor (GCD). In our examples:

• 7% as a fraction is \( \frac{7}{100} \). Since 7 is a prime number, it cannot be simplified further.
• 13% as a fraction is \( \frac{13}{100} \). 13 is also a prime number, so this fraction is already in its simplest form.

For fractions where both the numerator and denominator have common divisors, you would divide by the GCD to simplify. For instance, \( \frac{50}{100} \) simplifies to \( \frac{1}{2} \) because 50 and 100 can both be divided by 50.