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?
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 $1.1*10^2$