Rational Numbers and Their Decimal Expansions

The decimal expansion of the rational number $\frac{43}{2^4\times 5^3}$ will terminate after how many places of decimal?

Write down the decimal expansion of the rational number $\frac{19}{250}$.

Write $1215.8$ in the form of $\frac{p}{q},q\ne 0$ and $p,q$ are co-primes. What can you conclude about the denominators through this process?

Write $23.34$ in the form of $\frac{p}{q},q\ne 0$ and $p,q$ are co-primes. What can you conclude about the denominators through this process?

Write $0.4$ in the form of $\frac{p}{q},q\ne 0$ and $p,q$ are co-primes. What can you conclude about the denominators through this process?

Write $0.1255$ in the form of $\frac{p}{q},q\ne 0$ and $p,q$ are co-primes. What can you conclude about the denominators through this process?

Write $15.265$ in the form of $\frac{p}{q},q\ne 0$ and $p,q$ are co-primes. What can you conclude about the denominators through this process?

State whether the number $43.\overline{123456789}$ is rational or not? If it is rational, and expressed in form $\frac{p}{q}$, what can you say about the prime factors of $q?$

State whether the number $0.12012001200012000.......$ is rational or not? If it is rational, and expressed in form $\frac{p}{q}$, what can you say about the prime factors of $q?$

State whether the number $43.123456789$ is rational or not? If it is rational, and expressed in form $\frac{p}{q}$, what can you say about the prime factors of $q?$

Without performing division, state whether the rational number $\frac{77}{210}$ will have a terminating decimal form or non-terminating, repeating decimal.

Without performing division, state whether the rational number $\frac{36}{100}$ will have a terminating decimal form or non-terminating, repeating decimal.

Without performing division, state whether the rational number $\frac{9}{15}$ will have a terminating decimal form or non-terminating, repeating decimal.

Without performing division, state whether the rational number $\frac{129}{2^2{5}^7{7}^5}$ will have a terminating decimal form or non-terminating, repeating decimal.

Without performing division, state whether the rational number $\frac{23}{2^3{5}^2}$ will have a terminating decimal form or non-terminating, repeating decimal.

Without performing division, state whether the rational number $\frac{29}{343}$ will have a terminating decimal form or non-terminating, repeating decimal.

Write the rational number $\frac{80}{100}$ in the form of $\frac{p}{q}$, where $q$ is of the form $2^n{5}^m$ where $n$ and $m$ are non-negative integers and then write the number in its decimal form.

Write the rational number $\frac{14}{25}$ in the form of $\frac{p}{q}$, where $q$ is of the form $2^n{5}^m$ where $n$ and $m$ are non-negative integers and then write the number in its decimal form.

The decimal form of the rational number $\frac{100}{81}$ is 

If $\frac{p}{q}$ is a rational number, then what condition applies for $q$ when $\frac{p}{q}$ is a terminating decimal?