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What is the result of $$\frac{0.002843\cdot 12.80184}{0.00032}$$ with the correct number of significant digits?

In the multiplication above, both have $7$ significant digits I think. Therefore the result must have $7$ as well... which would be $0.036396$.

Then it is divided by $0.00032$, which has $6$ significant digits. So the result must have $6$ as well. The result is $113.738$.

But according to the website, this result is wrong. It doesn't tell me the answer, but it gives me the options:

  • $113.74$
  • $1.1\cdot10^2$
  • $113.7$
  • $113.73635$

My answer doesn't match any. I picked the last one and it was wrong.

What did I do incorrectly?

Saturn
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    Honestly, I feel there are various ways to interpret this (more of a science issue rather than hard math), but i'm thinking it might be that they consider the bottom, $0.00032=3.2\cdot10^{-4}$ as having only two significant digits. – Brent Jun 15 '15 at 05:07

1 Answers1

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Your error is that you're counting the trailing 0's as significant digits, when in fact they are not. They are simply placeholders.

0.002843 = 2.843E-3, so it has 4 significant digits. 12.80184 = 1.280184E1 so it has 7 significant digits.
Thus the product 0.002824 * 12.80184 = 0.0363956312 = 3.63956312E-2 We trim down to 4 significant figures (the smaller of 4 and 7) to get 3.640E-2 (rounding up because of the 5).

Then, we divide by .00032 which has 2 significant figures. 113.75, but we only have 2 significant figures (the smaller of 2 and 4) We get 110, but the last 0 is not significant. To denote this, we write 1.1E2, or $1.1*10^2$

Ethan
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