The decimal expansion of the rational number | vedclass

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

Question

(A) To find the decimal expansion,we express the denominator in the form $2^n \cdot 5^m$.The given number is $\frac{33}{2^2 \cdot 5^1}$.To make the po

Vedclass · Accepted Answer

two decimal places

Vedclass · Answer

(A) To find the decimal expansion,we express the denominator in the form $2^n \cdot 5^m$.The given number is $\frac{33}{2^2 \cdot 5^1}$.To make the powers of $2$ and $5$ equal,we multiply the numerator and denominator by $5^{(2-1)} = 5^1$.$\frac{33 \cdot 5}{2^2 \cdot 5^1 \cdot 5^1} = \frac{165}{2^2 \cdot 5^2} = \frac{165}{(2 \cdot 5)^2} = \frac{165}{10^2} = \frac{165}{100} = 1.65$.The decimal expansion terminates after $2$ decimal places.

The decimal expansion of the rational number $\frac{33}{2^{2} \cdot 5}$ will terminate after

Similar Questions

Every odd integer $a$ is in the form of $\ldots \ldots \ldots \ldots$ where,$k \in Z$.

For any positive integer $n$,prove that $n^{3}-n$ is divisible by $6$.

Find the smallest five-digit number which is exactly divisible by $15$,$55$,and $99$.

The length,breadth,and height of a prayer room are $15\,m$,$12\,m$,and $21\,m$ respectively. Determine the longest rod which can measure the three dimensions of the room exactly. (in $,m$)

Simplify: $\frac{1}{\sqrt{6}-\sqrt{5}}-\frac{3}{\sqrt{5}-\sqrt{2}}-\frac{4}{\sqrt{6}+\sqrt{2}}$

Vedclass Test Series

Exam Paper Generator

Online Exam Module