簡約 8.8510^{-12}(5)(1/(610^7)-1/(10^7))

解

簡約

8.85 \cdot 1 0^{- 12} (5) (\frac{1}{6 \cdot 1 0 ^{7}} - \frac{1}{1 0 ^{7}})

\frac{59}{8 \cdot 1 0 ^{19}} - \frac{177}{1 0 ^{19} \cdot 4}

十進法表記

0

解答ステップ

8.85 \cdot 1 0^{- 12} (5) (\frac{1}{6 \cdot 1 0 ^{7}} - \frac{1}{1 0 ^{7}})

規則を適用する:

(a) = a

(5) = 5

= 8.85 \cdot 1 0^{- 12} \cdot 5 (\frac{1}{6 \cdot 1 0 ^{7}} - \frac{1}{1 0 ^{7}})

数を乗じる:

8.85 \cdot 5 = 44.25

= 44.25 \cdot 1 0^{- 12} (\frac{1}{6 \cdot 1 0 ^{7}} - \frac{1}{1 0 ^{7}})

= 1 0^{- 12} \cdot 44.25 (\frac{1}{6 \cdot 1 0 ^{7}} - \frac{1}{1 0 ^{7}})

指数の規則を適用する:

a^{- b} = \frac{1}{a ^{b}}

1 0^{- 12} = \frac{1}{1 0 ^{12}}

= \frac{1}{1 0 ^{12}} \cdot 44.25 (\frac{1}{6 \cdot 1 0 ^{7}} - \frac{1}{1 0 ^{7}})

\frac{1}{1 0 ^{12}} \cdot 44.25 (\frac{1}{6 \cdot 1 0 ^{7}} - \frac{1}{1 0 ^{7}}) = \frac{44.25}{1 0 ^{12}} (\frac{1}{6 \cdot 1 0 ^{7}} - \frac{1}{1 0 ^{7}})

= \frac{44.25}{1 0 ^{12}} (\frac{1}{6 \cdot 1 0 ^{7}} - \frac{1}{1 0 ^{7}})

\frac{44.25}{1 0 ^{12}} = \frac{4425}{100 \cdot 1 0 ^{12}}

= \frac{4425}{100 \cdot 1 0 ^{12}} (\frac{1}{6 \cdot 1 0 ^{7}} - \frac{1}{1 0 ^{7}})

キャンセル

\frac{4425}{100 \cdot 1 0 ^{12}} : \frac{177}{4 \cdot 1 0 ^{12}}

= \frac{177}{4 \cdot 1 0 ^{12}} (\frac{1}{6 \cdot 1 0 ^{7}} - \frac{1}{1 0 ^{7}})

拡張

\frac{177}{4 \cdot 1 0 ^{12}} (\frac{1}{6 \cdot 1 0 ^{7}} - \frac{1}{1 0 ^{7}}) : \frac{59}{8 \cdot 1 0 ^{19}} - \frac{177}{1 0 ^{19} \cdot 4}

= \frac{59}{8 \cdot 1 0 ^{19}} - \frac{177}{1 0 ^{19} \cdot 4}