Find the number of zeros after decimal point in 0.2 25 ,given that log ⁡ 2 = 0.30101My attempt: I found the answer as 17.…Should we add 1 as 17 is the characteristic or leave it as 17?

Question

Find the number of zeros after decimal point in       0.2          25      ,given that   log  ⁡  2  =  0.30101My attempt: I found the answer as 17.…Should we add 1 as 17 is the characteristic or leave it as 17?

Amir Barajas · Accepted Answer

You&#039;ve found that       0.2          25        =      10          −      17.47      …      , so       10          −      18        &amp;lt;      0.2          25        &amp;lt;      10          −      17        , that is                              0.0          …          0                ⏟                            18             zéros        1  &amp;lt;      0.2          25        &amp;lt;                              0.0          …          0                ⏟                            17             zéros        1  ,so we conclude that there are   17 zéros after the decimal point.

e3r2a1cakCh7 · Accepted Answer

We have      log          10        ⁡      0.2          25        =  25  ⋅      log          10        ⁡      2    10    =  25  ⋅  (      log          10        ⁡  2  −  1  )  ≈  −  17.4743That gives, by monotinicity of   x  ↦      10          x       that      10          −      18        &amp;lt;      10          −      17.4743      …        =      0.2          25        &amp;lt;      10          −      17        ,hence       0.2          25       has 17 zeros after the decimal point, no need to add 1.

Find the number of zeros after decimal point in 0.2^(25) ,given that log2=0.30101

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