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

\(2.3 \overline{18}\)