(1.247 × 10–3) ÷ (2.9 × 10–2)

asked by guest
on Nov 19, 2024 at 6:49 am



You asked:

Evaluate the expression: \(\frac{1.247 \cdot 10 - 3}{2.9 \cdot 10 - 2}\)

MathBot Answer:

\[\frac{1.247 \cdot 10 - 3}{2.9 \cdot 10 - 2} = \frac{947}{2700} = 0.35\overline{074}\]

\[\begin{aligned}\frac{1.247 \cdot 10 - 3}{2.9 \cdot 10 - 2}& = \left(\left(1 + \frac{247}{1000}\right) \cdot 10 - 3\right) \cdot \frac{1}{\left(2 + \frac{9}{10}\right) \cdot 10 - 2}\\& = \left(\frac{1247}{1000} \cdot 10 - 3\right) \cdot \frac{1}{\left(2 + \frac{9}{10}\right) \cdot 10 - 2}\\& = \left(\frac{1247}{100} - 3\right) \cdot \frac{1}{\left(2 + \frac{9}{10}\right) \cdot 10 - 2}\\& = \frac{947}{100} \cdot \frac{1}{\left(2 + \frac{9}{10}\right) \cdot 10 - 2}\\& = \frac{947}{100} \cdot \frac{1}{\frac{29}{10} \cdot 10 - 2}\\& = \frac{947}{100} \cdot \frac{1}{29 - 2}\\& = \frac{947}{100} \cdot \frac{1}{27}\\& = \frac{947}{2700}\end{aligned}\]

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