5.27 *10^-3 - 3.42 *10^-4

asked by guest
on Nov 16, 2024 at 11:21 am



You asked:

Evaluate the expression: \(5.27 \cdot {10}^{-3} - 3.42 \cdot {10}^{-4}\)

MathBot Answer:

\[5.27 \cdot {10}^{-3} - 3.42 \cdot {10}^{-4} = \frac{77}{15625} = 0.004928\]

\[\begin{aligned}5.27 \cdot {10}^{-3} - 3.42 \cdot {10}^{-4}& = \left(5 + \frac{27}{100}\right) \cdot \frac{1}{10^{3}} - \left(3 + \frac{42}{100}\right) \cdot \frac{1}{10^{4}}\\& = \frac{527}{100} \cdot \frac{1}{10^{3}} - \left(3 + \frac{42}{100}\right) \cdot \frac{1}{10^{4}}\\& = \frac{527}{100} \cdot \frac{1}{1000} - \left(3 + \frac{42}{100}\right) \cdot \frac{1}{10^{4}}\\& = \frac{527}{100000} - \left(3 + \frac{42}{100}\right) \cdot \frac{1}{10^{4}}\\& = \frac{527}{100000} - \left(3 + \frac{21}{50}\right) \cdot \frac{1}{10^{4}}\\& = \frac{527}{100000} - \frac{171}{50} \cdot \frac{1}{10^{4}}\\& = \frac{527}{100000} - \frac{171}{50} \cdot \frac{1}{10000}\\& = \frac{527}{100000} - \frac{171}{500000}\\& = \frac{77}{15625}\end{aligned}\]

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