(6.02x10^23)(-5.11x10^-27)/-8.23x10^5

asked by guest
on Oct 23, 2024 at 1:18 am



You asked:

Evaluate the expression: \(\frac{6.02 \cdot {10}^{23} \cdot -5.11 \cdot {10}^{-27}}{-8.23} \cdot {10}^{5}\)

MathBot Answer:

\[\frac{6.02 \cdot {10}^{23} \cdot -5.11 \cdot {10}^{-27}}{-8.23} \cdot {10}^{5} = \frac{153811}{4115} \approx 37.37812879708383961117861482381531\]

\[\begin{aligned}\frac{6.02 \cdot {10}^{23} \cdot -5.11 \cdot {10}^{-27}}{-8.23} \cdot {10}^{5}& = \left(6 + \frac{2}{100}\right) \cdot 10^{23} \cdot -1 \cdot \left(5 + \frac{11}{100}\right) \cdot \frac{1}{10^{27}} \cdot \frac{1}{- \left(8 + \frac{23}{100}\right)} \cdot 10^{5}\\& = \left(6 + \frac{1}{50}\right) \cdot 10^{23} \cdot -1 \cdot \left(5 + \frac{11}{100}\right) \cdot \frac{1}{10^{27}} \cdot \frac{1}{- \left(8 + \frac{23}{100}\right)} \cdot 10^{5}\\& = \frac{301}{50} \cdot 10^{23} \cdot -1 \cdot \left(5 + \frac{11}{100}\right) \cdot \frac{1}{10^{27}} \cdot \frac{1}{- \left(8 + \frac{23}{100}\right)} \cdot 10^{5}\\& = \frac{301}{50} \cdot 100000000000000000000000 \cdot -1 \cdot \left(5 + \frac{11}{100}\right) \cdot \frac{1}{10^{27}} \cdot \frac{1}{- \left(8 + \frac{23}{100}\right)} \cdot 10^{5}\\& = \frac{301}{50} \cdot 100000000000000000000000 \cdot -1 \cdot \frac{511}{100} \cdot \frac{1}{10^{27}} \cdot \frac{1}{- \left(8 + \frac{23}{100}\right)} \cdot 10^{5}\\& = \frac{301}{50} \cdot 100000000000000000000000 \cdot -1 \cdot \frac{511}{100} \cdot \frac{1}{1000000000000000000000000000} \cdot \frac{1}{- \left(8 + \frac{23}{100}\right)} \cdot 10^{5}\\& = \frac{301}{50} \cdot 100000000000000000000000 \cdot -1 \cdot \frac{511}{100} \cdot \frac{1}{1000000000000000000000000000} \cdot \frac{1}{- \frac{823}{100}} \cdot 10^{5}\\& = \frac{301}{50} \cdot 100000000000000000000000 \cdot -1 \cdot \frac{511}{100} \cdot \frac{1}{1000000000000000000000000000} \cdot - \frac{100}{823} \cdot 10^{5}\\& = \frac{301}{50} \cdot 100000000000000000000000 \cdot -1 \cdot \frac{511}{100} \cdot \frac{1}{1000000000000000000000000000} \cdot - \frac{100}{823} \cdot 100000\\& = 602000000000000000000000 \cdot -1 \cdot \frac{511}{100} \cdot \frac{1}{1000000000000000000000000000} \cdot - \frac{100}{823} \cdot 100000\\& = -602000000000000000000000 \cdot \frac{511}{100} \cdot \frac{1}{1000000000000000000000000000} \cdot - \frac{100}{823} \cdot 100000\\& = \frac{-3076220000000000000000000}{1000000000000000000000000000} \cdot - \frac{100}{823} \cdot 100000\\& = - \frac{153811}{50000000} \cdot - \frac{100}{823} \cdot 100000\\& = \frac{153811}{411500000} \cdot 100000\\& = \frac{153811}{4115}\end{aligned}\]

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