What is this using scientific notation.....?

Question

(2.3 x 10^4) + (2.0 x 10^-3)=
I know that i must make the exponents the same,but i don't know if i'm doing it right.
please tell me how to do it (by hand plz)

also is this right?
(2.67 x 10^-3) - (9.5 x 10^-4)

Answer 1

In adding or subtracting two numbers in scientific notation, you want to make the two exponents equal. This usually means making the smaller exponent the same as the larger one*. To do so, move the decimal place 1 to the left for each 1 added to the exponent. For (2.3 x 10^4) + (2.0 x 10^-3):
Increase exponent of 2.0 x 10^-3 by 7 and move decimal 7 places left. Note that this dos not change the value of the term.
2.0 x 10^-3 = 0.0000002 x 10^4.
Then (2.3 x 10^4) + (0.0000002 x 10^4) = 2.3000002 x 10^4.
You second expression isn't "right" (meaning ready for addition or subtraction) because the exponents aren't the same. You should be able to fix this using the first case as an example.

*but not always. For (0.00003 x 10^6) + (2 x 10^1) you get 0.00005 x 10^6 (an ungainly way to express such a number) if you do, and 5 x 10^1 if you don't.