The sum 1. overline{23} + 3.2 is a . . . . . | vedclass

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(A) Let $x = 1. \overline{23} = 1.232323...$ Multiplying by $100$,we get $100x = 123.232323...$ Subtracting $x$ from $100x$,we get $99x = 122$,so $x =

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Rational

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(A) Let $x = 1. \overline{23} = 1.232323...$ Multiplying by $100$,we get $100x = 123.232323...$ Subtracting $x$ from $100x$,we get $99x = 122$,so $x = \frac{122}{99}$. Now,$3.2 = \frac{32}{10} = \frac{16}{5}$. The sum is $\frac{122}{99} + \frac{16}{5} = \frac{122 	imes 5 + 16 	imes 99}{99 	imes 5} = \frac{610 + 1584}{495} = \frac{2194}{495}$. Since the sum can be expressed in the form $\frac{p}{q}$ where $p$ and $q$ are integers and $q 
eq 0$,it is a rational number.

The sum $1. \overline{23} + 3.2$ is a . . . . . . number.

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