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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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 =

Vedclass · Accepted Answer

Rational

Vedclass · Answer

(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.

Similar Questions

Check whether $4^n$ can end with the digit $0$ for any positive integer $n$.

What type of decimal expansion is $0.9999...$? (Terminating,Non-terminating repeating,Non-terminating non-repeating)

If $a, b, c$ are distinct prime integers,then the ratio of their $HCF$ to their $LCM$ is:

The product of $HCF(a, b)$ and $LCM(a, b)$ is equal to:

For two positive integers $a$ and $b$,if $\text{HCF}(a, b) = 7$ and $\text{LCM}(a, b) = 385$,then find the product $a \times b$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module