bullfromist wrote:
wouldn't 10^-4 be .0010 since you move the decimal places 4 units to the right. Do we disregard the 0 next to the 10?
You are right that the decimal moves 4 places, but this is actually scientific notation, and what is omitted from the way it is written above is the 1* in front of the \(10^{-4}\). So when you see \(10^{-1}\), what you should be reading is \(1*10^{-4}\). The decimal is moved for the 1, not the 10. Similarly, what do you do if you have \(876.38*10^{-3}\) ? You move the decimal on the 876.38 to the left 3 places. \(876.38*10^{-3} = 0.87638\)
You can prove it to yourself in another way:
\(10^{-1} = \frac{1}{10} = 0.1\)
\(10^{-2} = \frac{1}{10^2} = 0.01\)
\(10^{-3} = \frac{1}{10^3} = 0.001\)
\(10^{-4} = \frac{1}{10^4} = 0.0001\)
so \(10^{-4}\) is a shorthand way of saying "divide by 10000". But what are we dividing by 10000? Whatever is multiplied in front of \(10^{-4}\). If there's nothing written in front, then it's the same as multiplying by 1, and we typically don't write it when things are multiplied by 1.
I hope that clears up the confusion
Cheers
_________________
Dave de Koos
GMAT aficionado