math theory

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write a rational and irrational number between 1.12301 and 1.1230101.

  • math theory -

    rational: 1.12301005
    for an irrational, try this:
    1.12301^2 = 1.2611514601
    1.1230101^2 = 1.261151684702

    So, pick any number in between those, which ends in 2,7 or 8 (so it cannot be a perfect square). So, if we choose

    (1.2611514601 + 1.261151684702)/2 = 1.261151572401

    then its √ will be between the two original numbers. So,

    √1.261151572401 = 1.12301004999999888692...

    Of course, we could have chosen something easy like

    1.12301 + π/10000000000000
    1.12301 + √2/100000000000000000

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