H K Dass, Rama Verma and, Bhagwat Swarup Sharma Solutions for Chapter: Number System, Exercise 4: EXERCISE

Write down the decimal expansion of the rational number which have terminating decimal expansion.

$\frac{19}{250}$

Write down the decimal expansion of the rational number which have terminating decimal expansion.

$\frac{23}{2048}$

Write down the decimal expansion of the rational number which have terminating decimal expansion.

$\frac{35}{800}$

Write down the decimal expansion of the rational number, $\frac{52}{2^3\times 5^4}$ which has terminating decimal expansion.

Which of the following decimal expansions are rational. If they are rational $\frac{p}{q}$, then write down the prime factors of $q$.

$11.214\overline{78}$

Which of the following decimal expansions are rational. If they are rational $\frac{p}{q}$, then write down the prime factors of $q$.

$12.\overline{123456789}$

Without actually performing the long division, find if $\frac{987}{10500}$ will have terminating or non-terminating (repeating) decimal expansion. Give reasons for your answer.

A rational number in its decimal expression $327.7081$. What can you say about the prime factors of $q,$ when this number is expressed in the form $\raisebox{1ex}{$p$}\!\left/ \!\raisebox{-1ex}{$q$}\right.$? Give reasons.