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Number systems — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsNumber systems1 Mark
MCQ
The smallest rational number by which $\frac{1}{3}$ should be multiplied so that its decimal expansion terminates after one place of decimal, is:
  • A
    $\frac{1}{10}$
  • B
    $\frac{3}{10}$
  • C
    $3$
  • D
    $30$
✓

Answer

  1. $\frac{3}{10}$
    Solution:
    $\frac{1}{3}=0.33333...$ (a Non - termnating number)
    Now, if we remove 3 from denominator it will terminate.
    So, if we multiply by $\frac{3}{10}$
    i.e. $\frac{1}{3}\times\frac{1}{3}=\frac{1}{10}=0.1$ ( terminates after one place of decimal)
    By multiplying by $\frac{1}{10},$ 3 does not replaces.
    By multiplying by 3, we get 1, which is not terminating after one place of decimal
    And, by multiplying by 30, we get 10, again not terminating after one palce of decimal.
    Hence, option (b) is correct.

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