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How Can I Find The Value Of (10 ^ -0.1)
(Without Using Calculator)

  • math -

    That's not possible. But 10^-1 is. You move your decimal to the left for negative exponents and you move your decimal to the right for positive exponents. If you had a value of 1 X 10^-2 for example you would move your decimal two places to the left which would equal .01 in decimal format. If you are in fact referring to scientific notation.

  • math -

    10^-.1
    = 1/10^.1

    So you want 1 divided by the tenth root of 10.

    In the days before calculators, we would now have to rely on log tables.
    We would have proceeded something like this

    let x = 10^(-1/10)
    logx = log [10^(-1/10) ]
    = (-1/10) log10
    = (-1/10)(1)
    = -1/10 or -.1
    = -1 + .9
    we would then find the "antilog of .9 from tables to get 7.9433

    the -1 would tell us to move the decimal one place to the left to get
    10^ -.1 as .79433

    log tables were only valid for positive logs, so if you had a negative, it was necessary to split it up into an integer + a positive decimal

    in our -1 + .9
    the -1 was called the characteristic, and the .9 is called the mantissa.
    The mantissa always had to be positive.
    so if we had something like
    logx = -3.35 it had to be changed to
    log = -4 + .65

    You are sooo fortunate to have calculators

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