Question 2 :
Which step in the following problem is wrong?<br/>$a = b = 1$<br/>$a = b$<br/>step-1: $a^2= ab$ <br/>step-2: $a^2\, -\, b^2\, =\, ab\, -\, b^2$<br/><span>step-3: $(a + b) (a - b) = b(a - b)$<br/>step-4: a + b = $\displaystyle \dfrac{b(a\, -\, b)}{a\, -\, b}$<br/>$a + b = b$<br/>$1 + 1 = 1$<br/>$2 = 1$</span>

Question 3 :
For any two rational numbers x and y which of the following are correct, if x is positive and y is negative?<br>$(1)$ x $&lt;$ y<br>$(2)$ x $=$ y<br>$(3)$ x $&gt;$ y.<br>

Question 5 :
<span>Convert the following fraction into simple decimal recurring form.</span><div><span>$\displaystyle \frac{1}{6}$= ?</span></div>

Question 6 :
If a number has a non-terminating and non-recurring decimal expansion, then it is.

Question 8 :
If P: every fraction is a rational number and Q: every rational number is a fraction, then which of the following options hold?

Question 9 :
<span>Find whether it is a terminating or a non-terminating decimal.</span><div>$0.3 \div 0.09$.</div>

Question 11 :
The decimal expansion of the rational number $\dfrac {33}{2^2\cdot 5}$ will terminate after:<br/>

Question 12 :
Which one of the following fractions is more than one-third ?

Question 14 :
If $x =\dfrac{p}{q}$ be a rational number such that the prime factorization of $q$ is not of the form $2^n 5^m$, where $n, m$ are non-negative integers. Then $x$ has a decimal expansion which is terminating.

Question 15 :
<p><span>State whether the statements given are True or False</span></p>Two rational with different numerators can never be equal

Question 16 :
If the numbers $\displaystyle \frac{4}{5}$, $81 \%$ and $0.801$ are arranged from smallest to largest, the correct order is:

Question 17 :
Consider the following statements :<br/>1. $\displaystyle \frac{1}{22}$ can not be written as terminating decimal <div><br/><span>2. $\displaystyle \frac{2}{15}$ can be written as a terminating decimal </span><br/></div><div><span><br/></span></div><div>3. $\displaystyle \frac{1}{16}$ can be written as a terminating decimal </div><div><br/>Which of the statements given above is/are correct ?</div>

Question 18 :
Which of the following statements are true or false?<br>The rational numbers $\dfrac {1}{3}$ and $\dfrac {-5}{2}$ are on opposite sides of $0$ on the number line.

Question 19 :
If $\displaystyle a=\left ( \frac{1}{10} \right )^{2},b=\frac{1}{5}$ and $\displaystyle c=\sqrt{\frac{1}{100}}$ then which of the following statements is correct?

Question 20 :
Without doing any actual division, find which of the following rational numbers have terminating decimal representation :<br>(i) $\displaystyle \dfrac{7}{16}$ (ii) $\displaystyle \dfrac{23}{125}$<br>(iii) $\displaystyle \dfrac{9}{14}$ (iv) $\displaystyle \dfrac{32}{45}$<br>(v) $\displaystyle \dfrac{43}{50}$ (vi) $\displaystyle \dfrac{17}{40}$<br>(vii) $\displaystyle \dfrac{61}{75}$ (viii) $\displaystyle \dfrac{123}{250}$