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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
    $\frac{1}{10}$
  • ✓
    $\frac{3}{10}$
  • C
    $3$
  • D
    $30$
✓

Answer

Correct option: B.
$\frac{3}{10}$
$\frac{1}{3}=0.33333... ($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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