Without actually performing the long division | vedclass

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

Question

(A) First,simplify the fraction to its lowest terms:$\frac{6}{15} = \frac{2 	imes 3}{5 	imes 3} = \frac{2}{5}$$A$ rational number $\frac{p}{q}$ has

Vedclass · Accepted Answer

Terminating decimal expansion

Vedclass · Answer

(A) First,simplify the fraction to its lowest terms:$\frac{6}{15} = \frac{2 	imes 3}{5 	imes 3} = \frac{2}{5}$$A$ rational number $\frac{p}{q}$ has a terminating decimal expansion if the prime factorization of the denominator $q$ is of the form $2^n 	imes 5^m$,where $n$ and $m$ are non-negative integers.Here,the denominator is $5$,which can be written as $2^0 	imes 5^1$.Since the denominator is in the form $2^n 	imes 5^m$,the decimal expansion of $\frac{6}{15}$ is terminating.

Without actually performing the long division,state whether the following rational number will have a terminating decimal expansion or a non-terminating repeating decimal expansion: $\frac{6}{15}$

Similar Questions

Prove that $3+2 \sqrt{5}$ is irrational.

The following real number has a decimal expansion as given below. Decide whether it is rational or not. If it is rational,and of the form $\frac{p}{q},$ what can you say about the prime factors of $q$?
$43.123456789$

Determine whether the rational number $\frac{77}{210}$ has a terminating or non-terminating repeating decimal expansion. If it is terminating,write down its decimal expansion.

Find the $LCM$ and $HCF$ of the following pairs of integers and verify that $LCM \times HCF =$ product of the two numbers $26$ and $91$.

The following real number has a decimal expansion as given below. Decide whether it is rational or not. If it is rational and of the form $\frac{p}{q}$,what can you say about the prime factors of $q$?
$0.120120012000120000 \ldots$

Vedclass Test Series

Exam Paper Generator

Online Exam Module