Without dividing, decide: does 23/2^2 × 5 have a terminating decimal expansion?

Yes, it terminates. Denominator = 2^2 × 5, only primes 2 and 5, so the expansion terminates. (23/20 = 1.15.)

Without dividing, decide: does $\frac{23}{2 ^{2} \times 5}$ have a terminating decimal expansion?

Class 10Decimal ExpansionsNumber Systems

Denominator =

2^{2} \times 5

, only primes 2 and 5, so the expansion terminates

. (\frac{23}{20} = 1.15.)

Answer: A) Yes, it terminates

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