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"Jupiter is approximately a sphere of radius $6.99 \times 10^7 \text{ m}$. (c) What is its volume in cubic kilometers? "

I have $V = \frac{4}{3}\pi r^3$. Then, $\frac{4}{3}\pi (6.99 \times 10^7\text{ m})^3$. Then, $2.93 \times 10^{22}\text{ m}^3$. Then, $10^{13}\text{ km}^3$.

But the software says the answer is "1.43e+15." I don't understand.

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    It's unclear what you think "sig figs" means. I would have guessed it was short for "significant figures," which refers to the number of digits in numbers such as 6.99 or 1.43. But your difficulties seem to be with every part of these exercises _except_ the significant figures. – 2017-01-24

3 Answers 3

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I've managed to detect your mistake. What you have done when you've inputted it in your calculator is done this: $$\frac{4}{3}\pi\times 6.99\times (10^7)^3\approx 2.9279644\times 10^{22}$$ Instead of the correct one: $$\frac{4}{3}\pi\times (6.99\times 10^7)^3\approx 1.4306063\times 10^{24}$$

Be sure to put parentheses where necessary. If you still cannot get this result on your calculator, please let me know.

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One of the steps requires you to calculate $(6.99 \times 10^7)^3$. It appears that you calculated $6.99 \times (10^7)^3$ instead, which is very different.

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This time I will try to break down the problem a little bit more clearly than with the area example, to hopefully help you understand this. I would highly recommend checking out some simple manipulation examples, for starters, Khan Academy on DA, Khan Academy on Sig. Figs, and Khan Academy on Scientific Notation. I think you need to work on your baseline understanding before attempting these results.

\begin{align} \frac{4}{3} \pi r^3 &= \frac{4}{3} \cdot \pi \cdot (6.99 \times 10^7 m )^3 \\ &= \frac{4}{3}\pi \cdot (6.99)^3 \times (10^7)^3 \times (m)^3 \\ &= \frac{4}{3}\pi \cdot (6.99 \cdot 6.99 \cdot 6.99) \times (10^{7 \cdot 3} )\times (m \cdot m \cdot m )\\ &= 1430 \times (10^{21}) \times (m\cdot m\cdot m) \\ &= (1.43 \times 10^3) \times 10^{21} \times (m\cdot m\cdot m) \\ &= 1.43 \times 10^{3 + 21}\times (m \cdot m\cdot m)\\ &= 1.43 \times 10^{24} \times m\cdot m \cdot m\\ &= 1.43 \times 10^{24} \times m\cdot m \cdot m \times (\frac{1000m}{1000m}) \\ &= 1.43 \times 10^{24} \times m\cdot m \cdot m \times (\frac{1km}{1000m}) \\ &= 1.43 \times 10^{24} \times m\cdot m \cdot m \times (\frac{1km}{1000m} \cdot \frac{1km}{1000m} \cdot \frac{1km}{1000m}) \\ &= 1.43 \times 10^{24} \times (\frac{1km \cdot m}{1000m} \cdot \frac{1km\cdot m}{1000m} \cdot \frac{1km\cdot m}{1000m}) \\ &= 1.43 \times 10^{24} \times (\frac{1km}{1000} \cdot \frac{1km}{1000} \cdot \frac{1km}{1000}) \\ &= 1.43 \times 10^{24} \times (\frac{1km}{10^3} \cdot \frac{1km}{10^3} \cdot \frac{1km}{10^3}) \\ &= 1.43 \times 10^{24} \times \frac{km^3}{(10^3)^3} \\ &= 1.43 \times \frac{10^{24}}{(10^3)^3} \times km^3 \\ &= 1.43 \times \frac{10^{24}}{10^9} \times km^3 \\ &= 1.43 \times 10^{24 - 9} \times km^3 \\ &= 1.43 \times 10^{15} km^3 \end{align}