MCQ
The decimal expansion of $\frac{21}{24}$ will terminate after :
- A$1$ decimal place
- BNone of these
- ✓$3$ decimal places
- D$2$ decimal places
✓
Answer
Correct option: C.
$3$ decimal places
$\frac{21}{24}=\frac{7}{8}=\frac{7}{2^3},$
Here, in the denominator of the given fraction, the highest power of prime factor $2$ is $3,$
therefore, the decimal expansion of the rational number $\frac{7}{2^3}$ will terminate after $3$ decimal places.
Here, in the denominator of the given fraction, the highest power of prime factor $2$ is $3,$
therefore, the decimal expansion of the rational number $\frac{7}{2^3}$ will terminate after $3$ decimal places.
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