Write 0.22% as a fraction in simplest form

Explanation

• Drop the % symbol and write 175 over 100

0.22% = \(\frac{0.22}{100}\)

To write this as an equivalent fraction of whole numbers, we need to move the decimal point in the numerator two places to the right. (Recall that to find the product of a decimal and 100, we simply move the decimal point two places to the right.) Therefore, it follows that \(\frac{100}{100}\) is the form of 1 that we should use to build \(\frac{0.22}{100}\).

• Multiply the fraction by a form of 1

\(\frac{0.22}{100}\) = \(\frac{0.22}{100} \cdot \frac{100}{100}\)

• Multiply the numerators and denominators

= \(\frac{0.22 \cdot 100}{100 \cdot 100} \)

= \(\frac{22}{10000}\)

• To simplify the fraction, factor 22 and 10,000. Remove the common factor of 2 from the numerator and denominator.

= \(\require{cancel}\frac{\cancel{2}^1 \cdot 11}{\cancel{2}_1 \cdot 5000}\)

= \(\frac{11}{5000}\)

Thus, 0.22% = \(\frac{11}{5000}\)