In 2007, 12.1% of the U.S. labour force belonged to a union. Write this percent as a fraction in simplest form.

Explanation

Strategy We will drop the % symbol and write the given number over 100. Then we will multiply the resulting fraction by a form of 1 and simplify, if possible.

WHY When writing a percent as a fraction, the numerator and denominator of the fraction should be whole numbers that have no common factors (other than 1).

Solution

• Drop the % symbol and write 12.1 over 100

12.1% = \(\frac{12.1}{100}\)

To write this as an equivalent fraction of whole numbers, we need to move the decimal point in the numerator one place to the right. (Recall that to find the product of a decimal and 10, we simply move the decimal point one place to the right.)
Therefore, it follows that \(\frac{10}{10}\) is the form of 1 that we should use to build \(\frac{12.1}{100}\).

• Multiply the fraction by a form of 1.

\(\frac{12.1}{100} = \frac{12.1}{100} \cdot \frac{10}{10}\)

• Multiply the numerators and multiply the denominators

=\(\frac{12.1 \cdot 10}{100 \cdot 10}\)

• Since 121 and 1,000 do not have any common factors (other than 1), the fraction is in simplest form

=\(\frac{121}{1000}\)

Thus 12.1% = \(\frac{121}{1000}\). This means that 121 out of every 1,000 workers in the U.S. labour force belonged to a union in 2007.