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Maths / Real Numbers / Decimal Expansion
QUESTION
 

What is the nature of the decimal expansion of the following?

1.large frac{13}{50}
2.large frac{13}{32}
3.large frac{13}{90}
EXPLANATION
Explain TypeExplanation Content
Text

(1) frac{13}{50}  =   As 50 = 5 X 5 X 2 =5^2 X  2  = Denominator has prime factors 2 and 5.  therefore Decimal representation of frac{13}{50} will be terminating. (2) frac{13}{32} = As 32 = 2^5 Denominator has 2 as a prime factor.  therefore Decimal representation of frac{13}{32} will be terminating.  (3) frac{13}{90}   As 90=2 X 3 X 3 X 5  = Denominator has prime factors other than 2 and 5. therefore Decimal representation of frac{13}{90} will not be terminating.

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