# Sig figs are impossible

Jupiter is approximately a sphere of radius $6.99 \times 10^7 \text{ m}$. (b) What is its surface area in square kilometers?

I have: $SA = 3\pi r^2 = 613.68 \times10^7 \text{ m}$. Then, $6.1368 \times10^9$. Then, $6.14 \times 10^6 \text{ km}$.

But the software says the answer is "6.14e+10". I don't understand.

• When you square the radius, you have to square the $10^7$ also. Also, the formula starts with $4$, not with $3$. – B. Goddard Jan 23 '17 at 21:56
• I don't understand. Does that mean 10^14? Then, 10^15? Then, 10^12? But that's not the answer... – user138342 Jan 23 '17 at 22:01
• Your kilometers are also squared. There are $10^6$ square meters in a square kilometer, not $10^3.$ – B. Goddard Jan 23 '17 at 22:04
• Where do 10^3 and 10^6 come from? Those aren't in the problem. – user138342 Jan 23 '17 at 22:31
• "Kilo" means "$10^3$". – B. Goddard Jan 23 '17 at 23:09

## 2 Answers

Surface Area of a sphere is $4\pi r^2$.

Let's plug-in an see what comes out:

\begin{align} 4\pi r^2 &= 4\pi(6.99 \cdot 10^7m)^2 \\ &= 4\pi(6.99)^2 \cdot (10^{7})^2 m^2\\ &= 4\pi(6.99)^2 \cdot(10^{14}) m^2\\ &= 613.994 \cdot (10^{14}) m^2\\ &= 6.14 \cdot 10^{16} m^2 \cdot \frac{1 km \cdot 1km}{10^3 m \cdot 10^3 m}\\ &= 6.14 \cdot 10^{10} km^2 \end{align}

• Where does 10^3 come from? I don't see a 3 anywhere else in the problem. – user138342 Jan 23 '17 at 22:29
• $1km = 10^3 m$. That's just a standard unit conversion. If that's confusing, may I suggest reading up on Dimensional Analysis – Dylan Jan 23 '17 at 22:30
• But isn't 10^3 x 10^3 - 100^6? Wouldn't that mean the answer is 0.614 x 10^10> – user138342 Jan 23 '17 at 22:59
• No. $10^3 \times 10^3 = 10^6$. What is $1000 \times 1000$? – Dylan Jan 23 '17 at 23:02
• Isn't the ^2 supposed to multiply throughout an equation? – user138342 Jan 23 '17 at 23:06

First of all you wrote the formula wrong. It must be $4\pi r^2$. If you just do the computition (YES you will square everything!) you will get $613 \times 10^{14}$ which is $6.13\times 10^{16}m^2$ from $m^2$ to $km^2$ you have a factor or $10^{-6}$ and if you multiply you will correctly get $6.13\times 10^{10}km^2$.

• Where does the -6 come from? I don't see 6 anywhere else. – user138342 Jan 23 '17 at 22:30
• it comes from the space.. how do you convert $m^2$ to $km^2$? if you dont know just type in googe! – Seyhmus Güngören Jan 23 '17 at 22:31
• But isn't 10^3 x 10^3 - 100^6? Wouldn't that mean the answer is 0.614 x 10^10? – user138342 Jan 23 '17 at 22:59