Adding and Subtracting Powers of 10

Question

I am entirely new to this subject and am already lost. The problem is Five x Ten to the power of Negative Two, + Four x Ten to the power of Negative Three. I was told that I have to make the exponents the same, and to do that I had to move one of the decimals, so I made Four x Ten to negative Two into 40 x Ten to negative Two. My final answer was 45 x 10 to the negative Two. Is this correct? If not how do I do this?

Answer 1

Five x Ten to the power of Negative Two, + Four x Ten to the power of Negative Three

... is a lot easier if you know the notation:

$$5 \times 10^{-2} + 4\times 10^{-3}$$

[And you should realize that $10^{-3}$ is less than $10^{-2}$. In fact $10^{-3} = 0.001$ and $10^{-2} = 0.01$.]

Then you can adjust the power-of-ten multipliers to get them the same, using for example

$$10^{-2} = 10 \times 10^{-3}$$

so

\begin{align}5 \times 10^{-2} + 4\times 10^{-3} &= 5 \times 10 \times 10^{-3} + 4\times 10^{-3} \\ &= 50 \times 10^{-3} + 4\times 10^{-3} \\ &= 54 \times 10^{-3} \\ &= 5.4 \times 10^{-2} \end{align}

So no. Your answer is not correct, and there are two problems, at least. First, it's way too big, and second, it doesn't match up with your problem statements. Probably because you're trying to keep track of this in words rather than numerical layout.