The decimal representation of 345679 /2²× 5⁵ Will be terminated after how many decimals places ??

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The decimal representation of 345679 /2²× 5⁵ Will be terminated after how many decimals places ??

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  1. Given : 345679 / (2² × 5⁵)

    To Find : The decimal representation will terminate after how many decimal places

    Solution:

    345679 / (2² × 5⁵)

    Multiply numerator and denominator by 2³

    = 345679 × 2³ / (2³ × 2² × 5⁵)

    = 345679 × 2³ / (2³ ⁺² × 5⁵)

    = 345679 × 2³ / (2⁵ × 5⁵)

    = 345679 × 2³ / (2× 5)⁵

    = 345679 × 2³ / (10)⁵

    = 345679 × 2³ / 100000

    The decimal representation will terminate after 5 decimal places.

    345679 × 2³ / 100000

    = 345679 × 8 / 100000

    = 2765432 / 100000

    = 27.65432

    The decimal representation will terminate after 5 decimal places.

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