Can anyone please explain how I got this wrong?

Question

Estimate (using scientific notation and rounding each entry to two digits) and round off answer to two digits: (0.000014 x 10^-12)(849,018 x 10⁴)

(A) 1.2x10^-9

(B) 1.2x10^-12

(C) 1.2x10^-2

(D) 1.2x10^-8

(E) none of the above

For this I got (A) 1.2x10^-9, but it was incorrect. Can someone please explain how I got this wrong?

Answer 1

(0.000014 x 10^-12)(849,018 x 10⁴)

Is better written as:

(1.4 x 10^-17) * (8.49018 x 10⁹)

because if you move the decimal in the first number 5 to the right you get 1.4, so you use your scientific notation rules to go from -12 to -17 in the exponent. You do a similar thing for the second one except this time you move the decimal 5 to the left so the exponent goes from 4 to 9.

Then you multiply 1.4 * 8.5 (approx.) to get ≈ 12, and you add the exponents together to get -8. 12 can be written as 1.2 x 10¹, so now you add that 1 to the -8 and you get 1.2 x 10^-7 as the final answer. I'm guessing that you subtracted 1 from -8 (and so you got 1.2 x 10^-9) instead of adding 1 to -8 in the exponent.

Answer 2

0.000014 · 849,018 is 11.9, and you need to add your exponents so you have -12+4=-8

This makes 11.9X10^-8, but that is not scientific notation because you can only have one digit before the decimal point.

When you change that to 1.19 (or 1.2), you are effectively dividing the number by 10. So you must multiply the power by 10 in order to balance that out. 10^-8 · 10¹ = 10^-7

So the final answer is 1.2x10^-7 (or choice E - none of the above)

My guess is that you moved the power down one instead of up one.

Answer 3

I cannot tell what you did wrong. I can tell you one way of answering.

0.000014 x 10^-12 = 1.4 x 10^-17

849,018 x 10⁴ = 8.49018 x 10⁹

1.4 x 8.5 = 11.90

11.90 x 10^-8

1.190 x 10^-7