2/5 rational number in p/q form ​

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2/5 rational number in p/q form

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Isabelle 1 month 2021-08-11T15:01:04+00:00 2 Answers 0 views 0

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    0
    2021-08-11T15:02:51+00:00

    2x/5

    Step-by-step explanation:-

    Let the rational number be , x

    2/5 of x = 2x/5

    P/Q form of 2/5 of a rational number is 2x/5

    0
    2021-08-11T15:02:52+00:00

    Well, I’ll try to explain. As for rationals with a finite decimal expansion, the job is simple. Select p and q from the decimal expansion, here “37818181”, find the next larger potency of 10, and that’s it:

    p=37818181,q=100000000

    (which cannot be further simplified, because q is only divisible by the primes 2 and 5, and neither 2 nor 5 divide p.)

    Or did you mean “what is the p/q form of 0.378181(81)…, i.e. a number with an endlessly repeating sequence of the digits 81? This case is a bit more difficult, but not really complicated.

    Let x=0.378181(81)…

    Then, 100·x=37.8181(81), and 10000·x=3781.8181(81)…

    Subtract 100·x from 10000·x:

    9900·x=3781.8181(81)…-37.8181(81)…=3781–37=3744

    Now divide by 9900:

    x=3744/9900

    and you have a p/q form for x. In this case, however, it can be simplified; apparently p and q can both be divided by 4, which gives another possible form:

    x=936/2475

    which can still be simplified further (because 9 divides 936 as well as 2475):

    x=104/275 or p=104, q=275

    as the final solution.

    Mark as BRAINLIST.

    For right answer

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