6.4 x 10^11 + 2.85 x 10^11 ( finding the sum written in scientific notation?)

Question

- 9.25 x 10^11 (my answer)
- 9.25 x 10^22
- 92.5 x 10^-10
- 92.5 x 10^12
3 x 10^20/ 4 x 10^5 (write in scientific notation)
- 7.5 x 10^3
- 0.75 x 10^4 (my answer)
- 7.5 x 10^14
- 7.5 x 10^15
(6.2 x 10^-8)(5 x 10^-2) *write in scientific notation*
- 3.1 x 10^16
- 3.1 x 10^-9
- 3.1 x 10^-11
- 3.1 x 10^-10 (my answer)
~Thanks! I really don't understand this

Answer 1

review scientific notation. There is a number and a power of 10.

the number must be between 1 and 10. (Less than 10)

When adding, the powers of 10 must be the same, just as you need a common denominator to add fractions. Then you can just add the numbers as usual, keeping the same power of 10.

When multiplying, you multiply the numbers, and add the exponents.

So, let's proceed.

6.4 x 10^11 + 2.85 x 10^11
The powers are the same, so just add.
(6.4+2.85)x10^11
9.25x10^11

3 x 10^20/ 4 x 10^5
divide numbers and subtract powers (because it's division, not multiplication)
(3/4)x10^(20-5)
= 0.75x10^15
But, the number has to be at least 1.0, so if we multiply it by 10, we have to also divide by 10 to keep things unchanged. Dividing by 10 means lowering the power by 1. So now we have
7.5x10^14

(6.2 x 10^-8)(5 x 10^-2)
(6.2*5)x10^(-8 + -2)
31.0x10^-10
But, the number must be less than 10, so we have to divide by 10, and raise the power to compensate:
3.1x10^-9

If things are still unclear, google scientific notation and you will find lots of other discussions. Maybe one of them will present things in a way that is clearer for you.