Repeating Decimals

EXAMPLE 5.30

Divide $43$ by $22$.

Notice that the differences of $120$ and $100$ repeat, so there is a repeat in the digits of the quotient; $54$ will repeat endlessly. The first decimal place in the quotient, $9$, is not part of the pattern. So,

$\frac{43}{22}=1.9 \overline{54}$

EXAMPLE 5.31

		$\frac{7}{8}+6.4$
Change $\frac{7}{8}$ to a decimal.		$0.875+6.4$
Add.		$7.275$

TRY IT 5.59

$2 . \overline{45}$

TRY IT 5.60

$2.3 \overline{18}$