# scientific notation

If I were trying to change a problem with exponents into a scientific notation how would I do that?

Example is $4(10^{50})^{100}$

I will have questions like this on an exam and I need to understand how to do it. Thank you.

• What does this have to do with normal distributions? Feb 28 '12 at 4:19
• @DilipSarwate I retagged OP's question.
– user2468
Feb 28 '12 at 4:28

Since $$(10^{50})^{100} = 10^{50 \times 100} = 10^{5000}$$ we have $$4(10^{50})^{100} = 4 \times 10^{5000}$$

• Yes, but do you have to break it down any farther? If it needs to be a single number?
– SNS
Feb 28 '12 at 4:21
• First let's make we using the same definition en.wikipedia.org/wiki/Scientific_notation
– user2468
Feb 28 '12 at 4:22
• I'd multiply out everything and then divide the result by the largest power of $10$ such that the quotient is a single digit. Example: $$4(10^{50})^{100} = 4(10^{5000})$$ Now, the largest such power of $10$ is $5000$.
– user2468
Feb 28 '12 at 4:24
• Nooo! $4\times 10^{5000} \color{red}{\neq} 40^{5000}$. Simpler example: $4 \times 10^2 = 400,$ whereas $40^2 = 1600$.
– user2468
Feb 28 '12 at 4:26
• That example 1.7x10^5 would fit better since it is a better approximation! Feb 28 '12 at 4:54