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 $\frac{19}{250}$.

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?

Which is the correct  decimal expansion of  $\frac{6}{15}$ ?

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

For the decimal expansion $27.\overline{142857}$, decide whether it is rational or not. If it is rational, then find the prime factors of its denominator.

For the decimal expansion $43.123456789$, decide whether it is rational or not. If it is rational, then find the prime factors of its denominator.

For the decimal expansion, $0.120120012000120000...$, decide whether it is rational or not. If it is rational, then write the note on prime factors of its denominator.

Write down the decimal expansion of $\frac{49}{500}$ and show whether it is terminating.

Write down the decimal expansion of $\frac{14588}{625}$ and show whether it is terminating.

Write down the decimal expansion of $\frac{13}{125}$ and show whether it is terminating.

Without actually performing long division method, state whether $\frac{7}{80}$ will have a terminating decimal expansion or a non-terminating recurring decimal expansion.

Without actually performing long division method, state whether $\frac{35}{50}$ will have a terminating decimal expansion or a non-terminating recurring decimal expansion.

Without actually performing long division method, state whether $\frac{129}{2^2\times 5^7\times 7^5}$ will have a terminating decimal expansion or a non-terminating recurring decimal expansion.

Without actually performing long division method, state whether $\frac{17}{6}$ will have a terminating decimal expansion or a non-terminating recurring decimal expansion.

Without actually performing long division method, state whether $\frac{23}{2^3\times 5^2}$ will have a terminating decimal expansion or a non-terminating recurring decimal expansion.

Without actually performing long division method, state whether $\frac{13}{3125}$ will have a terminating decimal expansion or a non-terminating recurring decimal expansion.

What can you say about the prime factors of the denominator of the rational number $43.\overline{123456789}$.

What can you say about the prime factors of the denominator of the number $34.12345$?