M L Aggarwal Solutions for Chapter: Real Numbers, Exercise 7: Chapter Test

Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating decimal expansion. Also write the decimal expansion which have terminating decimal expansions.

$\frac{231}{420}$

Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating decimal expansion. Also write the decimal expansion which have terminating decimal expansions.

$\frac{766}{1200}$

Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating decimal expansion. Also write the decimal expansion which have terminating decimal expansions.

$\frac{129}{2^2{5}^7{7}^3}$

Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating decimal expansion. Also write the decimal expansion which have terminating decimal expansions.

$\frac{72693}{4500}$

Write the denominator of the rational number $\frac{377}{4000}$ in the form $2^m{5}^n$ where $m, n$ are non-negative integers. Hence, write its decimal expansion without actual division.

The following real number have decimal expansion of $23.05\overline{4327}$. State whether they are rational or not. If they are rational and expressed in the form $\frac{p}{q}$, where $p, q$ are integers, $q\ne 0$ and $p, q$ are co-prime, then what can you say about the prime factors of $q$?

The following real number have decimal expansion of $174.3089$. State whether they are rational or not. If they are rational and expressed in the form $\frac{p}{q}$, where $p, q$ are integers, $q\ne 0$ and $p, q$ are co-prime, then what can you say about the prime factors of $q$?

The following real number have decimal expansion of $9.010010001....$. State whether they are rational or not. If they are rational and expressed in the form $\frac{p}{q}$, where $p, q$ are integers, $q\ne 0$ and $p, q$ are co-prime, then what can you say about the prime factors of $q$?