Classify the following numbers as rational or irrational with justification:
$(i)$ $\sqrt{\frac{9}{27}}$
$(ii)$ $\frac{\sqrt{28}}{\sqrt{343}}$
Classify the following numbers as rational or irrational with justification:
$(i)$ $\sqrt{\frac{9}{27}}$
$(ii)$ $\frac{\sqrt{28}}{\sqrt{343}}$
$(i)$ $\sqrt{\frac{9}{27}}=\frac{1}{\sqrt{3}},$ which of the quotient of a rational and an irrational number and therefore an irrational number.
$(ii)$ $\frac{\sqrt{28}}{\sqrt{343}}=\sqrt{\frac{4}{49}}=\frac{2}{7},$ which is a rational number.
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Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0$ :
$0.404040 \ldots$
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Simplify $: 2^{-3}+(0.01)^{-\frac{1}{2}}-(27)^{\frac{2}{3}}$
Simplify $: 2^{-3}+(0.01)^{-\frac{1}{2}}-(27)^{\frac{2}{3}}$
Fill in the blanks so as to make each of the following statements true (Final answer only)
The decimal expansion of $\frac{47}{50}$ is of $\ldots \ldots \ldots$ type.
Fill in the blanks so as to make each of the following statements true (Final answer only)
The decimal expansion of $\frac{47}{50}$ is of $\ldots \ldots \ldots$ type.
State whether the following statements are true or false? Justify your answer.
$\frac{\sqrt{15}}{\sqrt{3}}$ is written in the form $\frac{p}{q},$ where $q \neq 0$ so it is a rational number.
State whether the following statements are true or false? Justify your answer.
$\frac{\sqrt{15}}{\sqrt{3}}$ is written in the form $\frac{p}{q},$ where $q \neq 0$ so it is a rational number.