100×10³/3.14×10²

asked by guest
on Jan 19, 2025 at 8:18 am



You asked:

Evaluate the expression: \(\frac{100 \cdot {10}^{3}}{3.14} \cdot {10}^{2}\)

MathBot Answer:

\[\frac{100 \cdot {10}^{3}}{3.14} \cdot {10}^{2} = \frac{500000000}{157} = 3184713.\overline{375796178343949044585987261146496815286624203821656050955414012738853503184713}\]

\[\begin{aligned}\frac{100 \cdot {10}^{3}}{3.14} \cdot {10}^{2}& = 100 \cdot 10^{3} \cdot \frac{1}{3 + \frac{14}{100}} \cdot 10^{2}\\& = 100 \cdot 1000 \cdot \frac{1}{3 + \frac{14}{100}} \cdot 10^{2}\\& = 100 \cdot 1000 \cdot \frac{1}{3 + \frac{7}{50}} \cdot 10^{2}\\& = 100 \cdot 1000 \cdot \frac{1}{\frac{157}{50}} \cdot 10^{2}\\& = 100 \cdot 1000 \cdot \frac{50}{157} \cdot 10^{2}\\& = 100 \cdot 1000 \cdot \frac{50}{157} \cdot 100\\& = 100000 \cdot \frac{50}{157} \cdot 100\\& = \frac{5000000}{157} \cdot 100\\& = \frac{500000000}{157}\end{aligned}\]

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