簡約 8.854× 10^{-12}× (0.1)/(0.0005)

解

簡約

8.854 \cdot 1 0^{- 12} \cdot \frac{0.1}{0.0005}

\frac{4427}{5 ^{13} \cdot 2048}

十進法表記

1.7708 E - 9

解答ステップ

8.854 \cdot 1 0^{- 12} \cdot \frac{0.1}{0.0005}

\frac{0.1}{0.0005} = \frac{1}{0.005}

= 8.854 \cdot 1 0^{- 12} \cdot \frac{1}{0.005}

指数の規則を適用する:

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

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

= 8.854 \cdot \frac{1}{1 0 ^{12}} \cdot \frac{1}{0.005}

数を割る:

\frac{1}{0.005} = 200

= 8.854 \cdot \frac{1}{1 0 ^{12}} \cdot 200

8.854 \cdot \frac{1}{1 0 ^{12}} \cdot 200 = \frac{1770.8}{1 0 ^{12}}

= \frac{1770.8}{1 0 ^{12}}

\frac{1770.8}{1 0 ^{12}} = \frac{17708}{10 \cdot 1 0 ^{12}}

= \frac{17708}{10 \cdot 1 0 ^{12}}

10 \cdot 1 0^{12} = 1 0^{13}

= \frac{17708}{1 0 ^{13}}

因数

17708 : 2^{2} \cdot 4427

= \frac{2 ^{2} \cdot 4427}{1 0 ^{13}}

因数

1 0^{13} : 2^{13} \cdot 5^{13}

= \frac{2 ^{2} \cdot 4427}{2 ^{13} \cdot 5 ^{13}}

\frac{2 ^{2}}{2 ^{13}} = \frac{1}{2 ^{11}}

= \frac{4427}{2 ^{11} \cdot 5 ^{13}}

2^{11} = 2048

= \frac{4427}{5 ^{13} \cdot 2048}