Real numbers

Number Theory Level 2

The decimal expansion of $\frac { 317 }{ { 2 }^{ 4 }{ \times 5 }^{ 3 } }$ will terminate after how many places?

3 4 1 2

1 solution

Jared Low
Dec 28, 2014

$\frac{317}{2^4\times 5^3}=\frac{317\times 2}{2^4 \times 5^4}=\frac{634}{10^4}=0.0634$ . There are 4 decimal places, hence the answer is $\boxed{4}$

Actually theres a much easier and a faster way. Just look at the highest power of the two numbers in the denominator.

Ankit Vijay - 6 years, 5 months ago

Actually this is wrong. The result is 0.1585 Note that $\frac { 317 }{ 2^{ 4 }\times 5^{ 3 } } \neq \frac { 317\times 2 }{ 2^{ 4 }\times 5^{ 4 } }$ You have to Multiply the two sides of the fraction by 5: $\frac { 317 }{ 2^{ 4 }\times 5^{ 3 } } =\frac { 317\times 5 }{ 2^{ 4 }\times 5^{ 4 } } =\frac { 1585 }{ { 10 }^{ 4 } }$

Thiago Martinoni - 6 years, 3 months ago

Real numbers

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