Class 9 The World of Numbers Mock Test (CBSE)

Topics in The World of Numbers

• History of counting
• Zero and Brahmagupta's rules
• Integers and their arithmetic
• Fractions and rational numbers
• Rational numbers on the number line
• Density of rational numbers
• Irrational numbers and proof of irrationality
• Constructing irrational lengths
• Pi and Madhava's infinite series
• Terminating and repeating decimals
• Cyclic numbers
• Non-terminating non-repeating decimals
• Real numbers

The World of Numbers practice questions with answers

1. Q1Multiple choice·1 mark
   According to Brahmagupta's ancient rules of arithmetic regarding fortunes (positive numbers) and debts (negative numbers), what is the result of $0 - (-15)$?

   1. (a)$1$
   2. (b)$0$
   3. (c)$15$
   4. (d)$-15$
   Show answer and step marks

   1. Correct option: (c) $15$. Subtracting a debt (negative quantity) from zero yields a fortune (positive quantity), so $0 - (-15) = 15$.+1

   Answer: (c)
2. Q2Multiple choice·1 mark
   What is the product of the integers $-8$, $3$, and $-2$?

   1. (a)$-12$
   2. (b)$-48$
   3. (c)$12$
   4. (d)$48$
   Show answer and step marks

   1. Correct option: (d) $48$. Multiply the first two integers: $(-8) \times 3 = -24$. Then multiply by the third integer: $(-24) \times (-2) = 48$.+1

   Answer: (d)
3. Q3Multiple choice·1 mark
   Which of the following values of $p$ ensures that the decimal expansion of the rational number $\frac{p}{2^4 \cdot 5^2 \cdot 7}$ terminates after exactly $4$ decimal places?

   1. (a)$350$
   2. (b)$175$
   3. (c)$700$
   4. (d)$25$
   Show answer and step marks

   1. Correct option: (b) $175$. The denominator is $2800$, and $\frac{175}{2800} = \frac{1}{16} = \frac{625}{10^4} = 0.0625$ (exactly 4 places), whereas $\frac{350}{2800} = \frac{1}{8} = 0.125$, $\frac{700}{2800} = 0.25$ and $\frac{25}{2800} = \frac{1}{112}$ does not terminate.+1

   Answer: (b)
4. Q4Multiple choice·1 mark
   Which of the following numbers is a rational number?

   1. (a)$5 - \sqrt{2}$
   2. (b)$\sqrt{7 + 4\sqrt{3}}$
   3. (c)$\frac{3\sqrt{18}}{2\sqrt{2}}$
   4. (d)$\sqrt[3]{25}$
   Show answer and step marks

   1. Correct option: (c) $\frac{3\sqrt{18}}{2\sqrt{2}}$+1

   Answer: (c)
5. Q5Short answer·3 marks
   Represent the rational numbers $\frac{5}{3}$ and $-\frac{7}{3}$ on a number line.
   Show answer and step marks

   1. Draw a number line and mark integers at regular equal intervals.+1
   2. Divide each unit length between integers into 3 equal parts corresponding to the denominator 3.+1
   3. Mark $\frac{5}{3} = 1\frac{2}{3}$ at the 5th division to the right of $0$ (two-thirds of the way from $1$ to $2$).+0.5
   4. Mark $-\frac{7}{3} = -2\frac{1}{3}$ at the 7th division to the left of $0$ (one-third of the way from $-2$ to $-3$).+0.5

   Answer: With each unit divided into 3 equal parts, $\frac{5}{3}$ is the 5th division right of $0$ (between $1$ and $2$, at $1\frac{2}{3}$) and $-\frac{7}{3}$ is the 7th division left of $0$ (between $-2$ and $-3$, at $-2\frac{1}{3}$).

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