展開する (99(1/100-1/(2^{100)*100}))/2

解

展開する

\frac{99 ( \frac{1}{100} - \frac{1}{2 ^{100} \cdot 100} )}{2}

\frac{99}{200} - \frac{99}{2 ^{100} \cdot 200}

十進法表記

0.495

解答ステップ

\frac{99 ( \frac{1}{100} - \frac{1}{2 ^{100} \cdot 100} )}{2}

拡張

99 (\frac{1}{100} - \frac{1}{2 ^{100} \cdot 100}) : \frac{99}{100} - \frac{99}{2 ^{100} \cdot 100}

= \frac{\frac{99}{100} - \frac{99}{2 ^{100} \cdot 100}}{2}

分数の規則を適用する:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{\frac{99}{100} - \frac{99}{2 ^{100} \cdot 100}}{2} = \frac{\frac{99}{100}}{2} - \frac{\frac{99}{2 ^{100} \cdot 100}}{2}

= \frac{\frac{99}{100}}{2} - \frac{\frac{99}{2 ^{100} \cdot 100}}{2}

\frac{\frac{99}{100}}{2} = \frac{99}{200}

\frac{\frac{99}{2 ^{100} \cdot 100}}{2} = \frac{99}{2 ^{100} \cdot 200}

= \frac{99}{200} - \frac{99}{2 ^{100} \cdot 200}