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Maths / Real Numbers / Decimal Expansion
QUESTION
 

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

  • large frac{13}{50}
  •  large frac{13}{32}
  • large frac{13}{90}
    • EXPLANATION
    Explain TypeExplanation Content
    Text

    a) frac{13}{50}

    As 50=5X5X2=5^2X2

    =Denominator has prime factors 2 and 5

    therefore Decimal representation of frac{13}{50} will be terminating

    b) frac{13}{32}

    As 32=2^5

    =Denominator has 2 as a prime factor.

    therefore Decimal representation of frac{13}{32} will be terminating.

    c) frac{13}{90}

    As 90=2X3X3X5

    =Denominator has prime factors other than 2 and 5.

    therefore Decimal representation of frac{13}{90} will not be terminating.

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