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.
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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