How do I solve these problems involving significant figures?

Question

okay, i know some people might think this is easy stuff but im not a math person alrite...so here goes

first of all, how do you add & subtract 'in terms of significant figures'? not sure what this means...any examples?

2nd question is... why is this number (182000) when written in scientific notation, comes out to be 1.82 times 10? shouldn't it be 1.82 times 10 squared?

and how do you solve these two:

8.2 times 10 to the -2 PLUS 6.5 times 10 to the -1?

4.2 times 10 squared times 10 to the sixth DIVIDED BY
2.1 times 10 to the -6 times 10 to the sixth?

Thanks so much!!

Answer 1

when you add and subtract factoring in significant figures, after the process is done, you use the number of decimal places from the number with the least.

182000 is not 1.82x10. 1.82x10 is 182. and 1.82x10 squared is 1820. 182000 = 1.82x10^5

to add the first one, you need to make both values the same power of ten. so, .82x10^-1 + 6.5x10^-1 = 7.32x10^-1... which in addition with sig-figs will be 7.3x10^-1

i don't understand the last equation. times ten squared times ten to the sixth?

if both terms are x10^6 on top and bottom, they go away. so you're left with 4.2x10^2 / 2.1x10^-6 ... i'm going to factor a 2 out of the top. so it's [ 2 (2.1x10^2) / 2.1x10^6 ] . the 2.1s cancel out, and you subtract the exponents, to get [ 2 (1x10^-4) ] .. which is 2x10^-4

tadaa!

Answer 2

182000 = 1.82 * 10^5 not 1.82 * 10
8.2 * 10^ -2= .082 6.5 * 10^-1= .65 .082 +.65 = .732
4.2 * 10^2 = 42 2.1 * 10^-6 = .0000021 4.2/ .0000021= 2000000 or 2.0 * 10^6 this might help unless i'm wrong then it's just worthless information that I typed here to damage your brain.

Answer 3

(8.2 x 10 to the negative 2)(6.5 x 10 to the negative 1)=5.33 x 10 to the negative 2