Lesson 3, Topic 2
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# Square of Decimals and Fractions

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

### Example:

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

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