mathematics qs

[matttan]

I was doing the equation of E=mc^2

So its like this:

If M = 1kg and C=300 million m/s,

Then E= 1 x 300 million x 300 million = 90 000 million joules/90 billion joules

But the qs is,

If I convert c to 0.3 billion m/s,

then E = 1 x 0.3 billion x 0.3 billion = 0.09 billion joules

Why are both different? Can anyone explain the error?

Thanks (:

[Vid]

Neither of these answers are right. (3*10^8)^2 = 9*10^16

[CompuChip]

300 million x 300 million = (300 \times 10^6) \times (300 \times 10^6) = (300^2) \times 10^{12} = (9 \times 10^4) \times 10^{12} = 9 \times 10^{15}
while
0.3 billion x 0.3 billion = (0.3 \times 10^9) \times (0.3 \times 10^9) = (0.3^2) \times 10^{18} = (9 \times 10^{-2}) \times 10^{18}) = 9 \times 10^{15}.

I think your problem is that you are writing
300 million x 300 million = 90000 million
while it is actually
90000 million million.

Scientific notation is handy! :)