Write down the decimal expansion of the ratio | vedclass

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

Question

(C) rational number $\frac{p}{q}$ has a terminating decimal expansion if the prime factorization of the denominator $q$ is of the form $2^n 5^m$,where

Vedclass · Accepted Answer

Non-terminating

Vedclass · Answer

(C) rational number $\frac{p}{q}$ has a terminating decimal expansion if the prime factorization of the denominator $q$ is of the form $2^n 5^m$,where $n$ and $m$ are non-negative integers.In the given rational number $\frac{129}{2^{2} 5^{7} 7^{5}}$,the denominator contains a factor of $7^5$ in addition to $2$ and $5$.Since the prime factorization of the denominator includes a prime factor other than $2$ or $5$ (which is $7$),the decimal expansion of this rational number is non-terminating and repeating.Therefore,it does not have a terminating decimal expansion.

Write down the decimal expansion of the rational number $\frac{129}{2^{2} 5^{7} 7^{5}}$.

Similar Questions

Prove that $\frac{1}{\sqrt{2}}$ is an irrational number.

Prove that $6+\sqrt{2}$ is an irrational number.

Use Euclid's division lemma to show that the cube of any positive integer is of the form $9m, 9m+1$ or $9m+8$.

Show that any positive odd integer is of the form $6q+1$,$6q+3$,or $6q+5$,where $q$ is some integer.

An army contingent of $616$ members is to march behind an army band of $32$ members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march?

Vedclass Test Series

Exam Paper Generator

Online Exam Module