Home Class 9 Worksheets Number Systems

Chapter 1: Number Systems

Overview

This page provides comprehensive Chapter 1: Number Systems - Standard Worksheet - SJMaths. Standard level practice worksheet for Class 9 Number Systems.

Standard Level Worksheet

Back to Worksheets
  1. Question 1: Represent $\sqrt{9.3}$ on the number line.
    Solution:
    1. Draw a line segment AB = 9.3 units.
    2. Extend AB to C such that BC = 1 unit.
    3. Find the midpoint O of AC.
    4. Draw a semicircle with center O and radius OA.
    5. Draw a perpendicular at B intersecting the semicircle at D.
    6. BD = $\sqrt{9.3}$. With B as center and radius BD, draw an arc to cut the number line at E. Point E represents $\sqrt{9.3}$.
  2. Question 2: Simplify: $(256)^{-(4^{-3/2})}$
    Solution:
    First solve the exponent: $4^{-3/2} = \frac{1}{4^{3/2}} = \frac{1}{(2^2)^{3/2}} = \frac{1}{2^3} = \frac{1}{8}$.
    Now, expression becomes $(256)^{-1/8}$.
    $256 = 2^8$, so $(2^8)^{-1/8} = 2^{8 \times (-1/8)} = 2^{-1} = \frac{1}{2}$.
  3. Question 3: If $x = 3 + 2\sqrt{2}$, find the value of $x + \frac{1}{x}$.
    Solution:
    $\frac{1}{x} = \frac{1}{3+2\sqrt{2}} \times \frac{3-2\sqrt{2}}{3-2\sqrt{2}} = \frac{3-2\sqrt{2}}{9-8} = 3-2\sqrt{2}$.
    $x + \frac{1}{x} = (3+2\sqrt{2}) + (3-2\sqrt{2}) = 6$.
  4. Question 4: Express $0.00\overline{32}$ in the form $p/q$.
    Solution:
    Let $x = 0.003232\dots$
    $100x = 0.3232\dots$ (i)
    $10000x = 32.3232\dots$ (ii)
    Subtract (i) from (ii): $9900x = 32 \Rightarrow x = \frac{32}{9900} = \frac{8}{2475}$.
  5. Question 5: Visualize $4.\overline{26}$ on the number line up to 4 decimal places ($4.2626$).
    Solution:
    Use the process of successive magnification:
    1. Locate between 4 and 5.
    2. Magnify 4.2 to 4.3.
    3. Magnify 4.26 to 4.27.
    4. Magnify 4.262 to 4.263.
    5. Mark 4.2626.
  6. Question 6: Express $0.6 + 0.\overline{7} + 0.4\overline{7}$ in the form $p/q$.
    Solution:
    $0.6 = \frac{6}{10}$.
    $0.\overline{7} = \frac{7}{9}$.
    $0.4\overline{7} = \frac{47-4}{90} = \frac{43}{90}$.
    Sum $= \frac{6}{10} + \frac{7}{9} + \frac{43}{90} = \frac{54 + 70 + 43}{90} = \frac{167}{90}$.
  7. Question 7: Simplify: $4\sqrt{81} - 8(216)^{1/3} + 15(32)^{1/5} + \sqrt{225}$.
    Solution:
    $= 4(9) - 8(6^3)^{1/3} + 15(2^5)^{1/5} + 15$
    $= 36 - 8(6) + 15(2) + 15$
    $= 36 - 48 + 30 + 15 = 33$.
  8. Question 8: If $a = 2 + \sqrt{3}$, find the value of $a - \frac{1}{a}$.
    Solution:
    $\frac{1}{a} = \frac{1}{2+\sqrt{3}} \times \frac{2-\sqrt{3}}{2-\sqrt{3}} = 2-\sqrt{3}$.
    $a - \frac{1}{a} = (2+\sqrt{3}) - (2-\sqrt{3}) = 2 + \sqrt{3} - 2 + \sqrt{3} = 2\sqrt{3}$.
  9. Question 9: Represent $\sqrt{5}$ on the number line.
    Solution:
    Construct a right-angled triangle with base 2 units and height 1 unit.
    Hypotenuse $= \sqrt{2^2 + 1^2} = \sqrt{5}$.
    Using a compass, transfer this length to the number line starting from 0.
  10. Question 10: Find two irrational numbers between $0.1$ and $0.12$.
    Solution:
    Irrational numbers are non-terminating and non-repeating.
    Example 1: $0.1010010001\dots$
    Example 2: $0.110110011000\dots$
Previous Worksheet Next Worksheet