Square of Decimals and Fractions

To find the square of a decimal or fraction, multiply the decimal or fraction by itself.

Worked Example 3.2.1:

Find the square of the following

a.    (0.5)²

b.    (16.2)²

c.    \( \left ( \frac{5}{6} \right)^2\)

d.    \( \left ( \frac{1}{4} \right)^2\)

e. \( \left (\scriptsize 3 \frac{1}{3} \right)^2\)

Solution:

a. \( \scriptsize (0.5)^2 = 0.5 \: \times \: 0.5 \)

= \( \frac{5}{10} \: \times \: \frac{5}{10}\\ = \frac{25}{100} \\ = \scriptsize 0.25 \)

b. \( \scriptsize (16.2)^2 = 16.2 \: \times \: 16.2 \)

= \( \frac{162}{10} \: \times \: \frac{162}{10}\\ = \frac{26,244}{100} \\ = \scriptsize 262.44 \)

c. \( \left ( \frac{5}{6} \right)^2 \\ = \frac{5}{6} \: \times \: \frac{5}{6} \\ = \frac{25}{36}\)

d. \( \left ( \frac{1}{4} \right)^2 \\ = \frac{1}{4} \: \times \: \frac{1}{4} \\ = \frac{1 \: \times \: 1}{4 \: \times \: 4}\\ = \frac{1}{16}\)

e. \( \left (\scriptsize 3 \frac{1}{3} \right)^2 \\ =\left ( \frac{10}{3} \right)^2 \\ = \frac{10}{3} \: \times \: \frac{10}{3} \\ = \frac{10 \: \times \: 10}{3 \: \times \: 3}\\ = \frac{100}{9} \\ = \scriptsize 11 \frac{1}{9}\)