2.005 / 2.78

asked by guest
on Sep 22, 2024 at 4:23 am



You asked:

Evaluate the expression: \(\frac{2.005}{2.78}\)

MathBot Answer:

\[\frac{2.005}{2.78} = \frac{401}{556} = 0.72\overline{1223021582733812949640287769784172661870503597}\]

\[\begin{aligned}\frac{2.005}{2.78}& = \left(2 + \frac{5}{1000}\right) \cdot \frac{1}{2 + \frac{78}{100}}\\& = \left(2 + \frac{1}{200}\right) \cdot \frac{1}{2 + \frac{78}{100}}\\& = \frac{401}{200} \cdot \frac{1}{2 + \frac{78}{100}}\\& = \frac{401}{200} \cdot \frac{1}{2 + \frac{39}{50}}\\& = \frac{401}{200} \cdot \frac{1}{\frac{139}{50}}\\& = \frac{401}{556}\end{aligned}\]

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