簡約 24001/1000(1^2)/(2.54^2)*1/(4.448)

解

簡約

2400 \cdot \frac{1}{1000} \cdot \frac{1 ^{2}}{2.5 4 ^{2}} \cdot \frac{1}{4.448}

0.08363 \dots

解答ステップ

2400 \cdot \frac{1}{1000} \cdot \frac{1 ^{2}}{2.5 4 ^{2}} \cdot \frac{1}{4.448}

指数の規則を適用する:

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

\frac{1 ^{2}}{2.5 4 ^{2}} = (\frac{1}{2.54})^{2}

= 2400 (\frac{1}{2.54})^{2} \frac{1}{1000} \cdot \frac{1}{4.448}

(\frac{1}{2.54})^{2} = \frac{1}{2.5 4 ^{2}}

= 2400 \cdot \frac{1}{1000} \cdot \frac{1}{4.448} \cdot \frac{1}{2.5 4 ^{2}}

分数を乗じる:

a \cdot \frac{b}{c} \cdot \frac{d}{e} = \frac{a \cdot b \cdot d}{c \cdot e}

= \frac{1 \cdot 1 \cdot 1 \cdot 2400}{1000 \cdot 2.5 4 ^{2} \cdot 4.448}

数を乗じる:

1 \cdot 1 \cdot 1 \cdot 2400 = 2400

= \frac{2400}{1000 \cdot 2.5 4 ^{2} \cdot 4.448}

数を乗じる:

1000 \cdot 4.448 = 4448

= \frac{2400}{4448 \cdot 2.5 4 ^{2}}

共通因数を約分する:

32

= \frac{75}{139 \cdot 2.5 4 ^{2}}

139 \cdot 2.5 4^{2} = 896.7724

= \frac{75}{896.7724}

数を割る:

\frac{75}{896.7724} = 0.08363 \dots

= 0.08363 \dots