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Calculate 0.5 divided by 0.0001 using scientific notation.

Mathematics

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Answer

The solution shows the calculation of 0.50.0001\frac{0.5}{0.0001} using scientific notation.

Step-by-step solution

5 steps
  1. Convert the numbers to scientific notation.

    0.5=5×10−10.5 = 5 \times 10^{-1} 0.0001=1×10−40.0001 = 1 \times 10^{-4}
  2. Rewrite the division using scientific notation.

    0.50.0001=5×10−11×10−4\frac{0.5}{0.0001} = \frac{5 \times 10^{-1}}{1 \times 10^{-4}}
  3. Separate the numerical parts and the powers of 10.

    51×10−110−4\frac{5}{1} \times \frac{10^{-1}}{10^{-4}}
  4. Simplify the numerical part and use the exponent rule aman=am−n\frac{a^m}{a^n} = a^{m-n} for the powers of 10.

    5×10−1−(−4)5 \times 10^{-1 - (-4)} 5×10−1+45 \times 10^{-1 + 4} 5×1035 \times 10^{3}
  5. Convert the scientific notation back to standard form.

    5×103=5×1000=50005 \times 10^{3} = 5 \times 1000 = 5000

    The final result of the calculation is 5000. The units "J" and "Kg" shown at the bottom are not relevant to this calculation unless it's part of a larger problem where these units apply to other quantities.

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