2.079443+(9.2−8)(0.117782)+(9.2−8)(9.2−9)(−0.006432)+(9.2−8)(9.2−9)(9.2−9.5)(−0.002310)

asked by guest
on Dec 26, 2024 at 8:50 am



You asked:

Evaluate the expression: \(2.079443 + \left(9.2 - 8\right) \cdot 0.117782 + \left(9.2 - 8\right) \left(9.2 - 9\right) \cdot -0.006432 + \left(9.2 - 8\right) \left(9.2 - 9\right) \left(9.2 - 9.5\right) \cdot -0.002310\)

MathBot Answer:

\[2.079443 + \left(9.2 - 8\right) \cdot 0.117782 + \left(9.2 - 8\right) \left(9.2 - 9\right) \cdot -0.006432 + \left(9.2 - 8\right) \left(9.2 - 9\right) \left(9.2 - 9.5\right) \cdot -0.002310 = \frac{55485101}{25000000} = 2.21940404\]

\[\begin{aligned}2.079443 + \left(9.2 - 8\right) \cdot 0.117782 + \left(9.2 - 8\right) \left(9.2 - 9\right) \cdot -0.006432 + \left(9.2 - 8\right) \left(9.2 - 9\right) \left(9.2 - 9.5\right) \cdot -0.002310& = 2 + \frac{79443}{1000000} + \left(9 + \frac{2}{10} - 8\right) \cdot \frac{117782}{1000000} + \left(9 + \frac{2}{10} - 8\right) \cdot \left(9 + \frac{2}{10} - 9\right) \cdot -1 \cdot \frac{6432}{1000000} + \left(9 + \frac{2}{10} - 8\right) \cdot \left(9 + \frac{2}{10} - 9\right) \cdot \left(9 + \frac{2}{10} - \left(9 + \frac{5}{10}\right)\right) \cdot -1 \cdot \frac{231}{100000}\\& = 2 + \frac{79443}{1000000} + \left(9 + \frac{1}{5} - 8\right) \cdot \frac{117782}{1000000} + \left(9 + \frac{2}{10} - 8\right) \cdot \left(9 + \frac{2}{10} - 9\right) \cdot -1 \cdot \frac{6432}{1000000} + \left(9 + \frac{2}{10} - 8\right) \cdot \left(9 + \frac{2}{10} - 9\right) \cdot \left(9 + \frac{2}{10} - \left(9 + \frac{5}{10}\right)\right) \cdot -1 \cdot \frac{231}{100000}\\& = 2 + \frac{79443}{1000000} + \left(\frac{46}{5} - 8\right) \cdot \frac{117782}{1000000} + \left(9 + \frac{2}{10} - 8\right) \cdot \left(9 + \frac{2}{10} - 9\right) \cdot -1 \cdot \frac{6432}{1000000} + \left(9 + \frac{2}{10} - 8\right) \cdot \left(9 + \frac{2}{10} - 9\right) \cdot \left(9 + \frac{2}{10} - \left(9 + \frac{5}{10}\right)\right) \cdot -1 \cdot \frac{231}{100000}\\& = 2 + \frac{79443}{1000000} + \frac{6}{5} \cdot \frac{117782}{1000000} + \left(9 + \frac{2}{10} - 8\right) \cdot \left(9 + \frac{2}{10} - 9\right) \cdot -1 \cdot \frac{6432}{1000000} + \left(9 + \frac{2}{10} - 8\right) \cdot \left(9 + \frac{2}{10} - 9\right) \cdot \left(9 + \frac{2}{10} - \left(9 + \frac{5}{10}\right)\right) \cdot -1 \cdot \frac{231}{100000}\\& = 2 + \frac{79443}{1000000} + \frac{706692}{5} \cdot \frac{1}{1000000} + \left(9 + \frac{2}{10} - 8\right) \cdot \left(9 + \frac{2}{10} - 9\right) \cdot -1 \cdot \frac{6432}{1000000} + \left(9 + \frac{2}{10} - 8\right) \cdot \left(9 + \frac{2}{10} - 9\right) \cdot \left(9 + \frac{2}{10} - \left(9 + \frac{5}{10}\right)\right) \cdot -1 \cdot \frac{231}{100000}\\& = 2 + \frac{79443}{1000000} + \frac{176673}{1250000} + \left(9 + \frac{2}{10} - 8\right) \cdot \left(9 + \frac{2}{10} - 9\right) \cdot -1 \cdot \frac{6432}{1000000} + \left(9 + \frac{2}{10} - 8\right) \cdot \left(9 + \frac{2}{10} - 9\right) \cdot \left(9 + \frac{2}{10} - \left(9 + \frac{5}{10}\right)\right) \cdot -1 \cdot \frac{231}{100000}\\& = 2 + \frac{79443}{1000000} + \frac{176673}{1250000} + \left(9 + \frac{1}{5} - 8\right) \cdot \left(9 + \frac{2}{10} - 9\right) \cdot -1 \cdot \frac{6432}{1000000} + \left(9 + \frac{2}{10} - 8\right) \cdot \left(9 + \frac{2}{10} - 9\right) \cdot \left(9 + \frac{2}{10} - \left(9 + \frac{5}{10}\right)\right) \cdot -1 \cdot \frac{231}{100000}\\& = 2 + \frac{79443}{1000000} + \frac{176673}{1250000} + \left(\frac{46}{5} - 8\right) \cdot \left(9 + \frac{2}{10} - 9\right) \cdot -1 \cdot \frac{6432}{1000000} + \left(9 + \frac{2}{10} - 8\right) \cdot \left(9 + \frac{2}{10} - 9\right) \cdot \left(9 + \frac{2}{10} - \left(9 + \frac{5}{10}\right)\right) \cdot -1 \cdot \frac{231}{100000}\\& = 2 + \frac{79443}{1000000} + \frac{176673}{1250000} + \frac{6}{5} \cdot \left(9 + \frac{2}{10} - 9\right) \cdot -1 \cdot \frac{6432}{1000000} + \left(9 + \frac{2}{10} - 8\right) \cdot \left(9 + \frac{2}{10} - 9\right) \cdot \left(9 + \frac{2}{10} - \left(9 + \frac{5}{10}\right)\right) \cdot -1 \cdot \frac{231}{100000}\\& = 2 + \frac{79443}{1000000} + \frac{176673}{1250000} + \frac{6}{5} \cdot \left(9 + \frac{1}{5} - 9\right) \cdot -1 \cdot \frac{6432}{1000000} + \left(9 + \frac{2}{10} - 8\right) \cdot \left(9 + \frac{2}{10} - 9\right) \cdot \left(9 + \frac{2}{10} - \left(9 + \frac{5}{10}\right)\right) \cdot -1 \cdot \frac{231}{100000}\\& = 2 + \frac{79443}{1000000} + \frac{176673}{1250000} + \frac{6}{5} \cdot \left(\frac{46}{5} - 9\right) \cdot -1 \cdot \frac{6432}{1000000} + \left(9 + \frac{2}{10} - 8\right) \cdot \left(9 + \frac{2}{10} - 9\right) \cdot \left(9 + \frac{2}{10} - \left(9 + \frac{5}{10}\right)\right) \cdot -1 \cdot \frac{231}{100000}\\& = 2 + \frac{79443}{1000000} + \frac{176673}{1250000} + \frac{6}{5} \cdot \frac{-1}{5} \cdot \frac{6432}{1000000} + \left(9 + \frac{2}{10} - 8\right) \cdot \left(9 + \frac{2}{10} - 9\right) \cdot \left(9 + \frac{2}{10} - \left(9 + \frac{5}{10}\right)\right) \cdot -1 \cdot \frac{231}{100000}\\& = 2 + \frac{79443}{1000000} + \frac{176673}{1250000} + \frac{6}{5} \cdot \frac{-1}{5} \cdot \frac{201}{31250} + \left(9 + \frac{2}{10} - 8\right) \cdot \left(9 + \frac{2}{10} - 9\right) \cdot \left(9 + \frac{2}{10} - \left(9 + \frac{5}{10}\right)\right) \cdot -1 \cdot \frac{231}{100000}\\& = 2 + \frac{79443}{1000000} + \frac{176673}{1250000} + \frac{6}{25} \cdot -1 \cdot \frac{201}{31250} + \left(9 + \frac{2}{10} - 8\right) \cdot \left(9 + \frac{2}{10} - 9\right) \cdot \left(9 + \frac{2}{10} - \left(9 + \frac{5}{10}\right)\right) \cdot -1 \cdot \frac{231}{100000}\\& = 2 + \frac{79443}{1000000} + \frac{176673}{1250000} - \frac{603}{390625} + \left(9 + \frac{2}{10} - 8\right) \cdot \left(9 + \frac{2}{10} - 9\right) \cdot \left(9 + \frac{2}{10} - \left(9 + \frac{5}{10}\right)\right) \cdot -1 \cdot \frac{231}{100000}\\& = 2 + \frac{79443}{1000000} + \frac{176673}{1250000} - \frac{603}{390625} + \left(9 + \frac{1}{5} - 8\right) \cdot \left(9 + \frac{2}{10} - 9\right) \cdot \left(9 + \frac{2}{10} - \left(9 + \frac{5}{10}\right)\right) \cdot -1 \cdot \frac{231}{100000}\\& = 2 + \frac{79443}{1000000} + \frac{176673}{1250000} - \frac{603}{390625} + \left(\frac{46}{5} - 8\right) \cdot \left(9 + \frac{2}{10} - 9\right) \cdot \left(9 + \frac{2}{10} - \left(9 + \frac{5}{10}\right)\right) \cdot -1 \cdot \frac{231}{100000}\\& = 2 + \frac{79443}{1000000} + \frac{176673}{1250000} - \frac{603}{390625} + \frac{6}{5} \cdot \left(9 + \frac{2}{10} - 9\right) \cdot \left(9 + \frac{2}{10} - \left(9 + \frac{5}{10}\right)\right) \cdot -1 \cdot \frac{231}{100000}\\& = 2 + \frac{79443}{1000000} + \frac{176673}{1250000} - \frac{603}{390625} + \frac{6}{5} \cdot \left(9 + \frac{1}{5} - 9\right) \cdot \left(9 + \frac{2}{10} - \left(9 + \frac{5}{10}\right)\right) \cdot -1 \cdot \frac{231}{100000}\\& = 2 + \frac{79443}{1000000} + \frac{176673}{1250000} - \frac{603}{390625} + \frac{6}{5} \cdot \left(\frac{46}{5} - 9\right) \cdot \left(9 + \frac{2}{10} - \left(9 + \frac{5}{10}\right)\right) \cdot -1 \cdot \frac{231}{100000}\\& = 2 + \frac{79443}{1000000} + \frac{176673}{1250000} - \frac{603}{390625} + \frac{6}{5} \cdot \frac{1}{5} \cdot \left(9 + \frac{2}{10} - \left(9 + \frac{5}{10}\right)\right) \cdot -1 \cdot \frac{231}{100000}\\& = 2 + \frac{79443}{1000000} + \frac{176673}{1250000} - \frac{603}{390625} + \frac{6}{5} \cdot \frac{1}{5} \cdot \left(9 + \frac{1}{5} - \left(9 + \frac{5}{10}\right)\right) \cdot -1 \cdot \frac{231}{100000}\\& = 2 + \frac{79443}{1000000} + \frac{176673}{1250000} - \frac{603}{390625} + \frac{6}{5} \cdot \frac{1}{5} \cdot \left(9 + \frac{1}{5} - \left(9 + \frac{1}{2}\right)\right) \cdot -1 \cdot \frac{231}{100000}\\& = 2 + \frac{79443}{1000000} + \frac{176673}{1250000} - \frac{603}{390625} + \frac{6}{5} \cdot \frac{1}{5} \cdot \left(9 + \frac{1}{5} - \frac{19}{2}\right) \cdot -1 \cdot \frac{231}{100000}\\& = 2 + \frac{79443}{1000000} + \frac{176673}{1250000} - \frac{603}{390625} + \frac{6}{5} \cdot \frac{1}{5} \cdot \left(\frac{46}{5} - \frac{19}{2}\right) \cdot -1 \cdot \frac{231}{100000}\\& = 2 + \frac{79443}{1000000} + \frac{176673}{1250000} - \frac{603}{390625} + \frac{6}{5} \cdot \frac{1}{5} \cdot - \frac{3}{10} \cdot -1 \cdot \frac{231}{100000}\\& = 2 + \frac{79443}{1000000} + \frac{176673}{1250000} - \frac{603}{390625} + \frac{6}{25} \cdot - \frac{3}{10} \cdot -1 \cdot \frac{231}{100000}\\& = 2 + \frac{79443}{1000000} + \frac{176673}{1250000} - \frac{603}{390625} - - \frac{9}{125} \cdot \frac{231}{100000}\\& = 2 + \frac{79443}{1000000} + \frac{176673}{1250000} - \frac{603}{390625} + \frac{9}{125} \cdot \frac{231}{100000}\\& = 2 + \frac{79443}{1000000} + \frac{176673}{1250000} - \frac{603}{390625} + \frac{2079}{12500000}\\& = \frac{2079443}{1000000} + \frac{176673}{1250000} - \frac{603}{390625} + \frac{2079}{12500000}\\& = \frac{11103907}{5000000} - \frac{603}{390625} + \frac{2079}{12500000}\\& = \frac{55480943}{25000000} + \frac{2079}{12500000}\\& = \frac{55485101}{25000000}\end{aligned}\]

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