Question

Write whether the rational number 71/500 will have terminating decimal expansion or a non
terminating repeating decimal expansion.
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Answer 1

Step-by-step explanation:

$500 \div 11 = 45.4545455$

yes, it has terminating decimal expansion because 500 has factor of 2 and 5 . from rule, let the denominator of any fraction be any number, if it has the factor of 2 and their decimal expansion must be terminating ...

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Answer 2

Answer:

0.034

Step-by-step explanation:

If a fraction , in its lowest terms , denominator

has no other prime factors except 2 and 5

it can be expressed as a terminating

decimal.First we have write 51 / 1500 in it's

least form

51 / 1500 = ( 3 × 17 ) / ( 3 × 500 )

After cancellation , we get

51 / 1500 = 17 / 500

denominator = 500

= 2 × 2 × 5 × 5 × 5

Therefore ,

The denominator has no other

prime factors except 2 and 5 .

51 / 1500 is terminating decimal.

51 / 1500 = 17 / ( 2^2 × 5^3 )

= ( 17 × 2 ) / ( 2^3 × 5^3 )

= 34 / ( 2 ^3 × 5^3 )

= 0.034 ( terminating decimal )

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