Quick Significant Figures Problem

[Lori]

Homework Statement

)(9.66x10^-1) + (5.1x10^2) -8.77+2.8 ) / ((8.333x10^-2)(3.001))

Homework Equations

None

The Attempt at a Solution

my answer does not match the answer key which is 2.0 x 10^3.[/B]
When i did the problem , i ended up get 3 SF answer. The numerator simplies to 504.996 where the sigfigs should be 3 because 0 is the least number of decimals. The denominator is simplified to 0.25007333 where the sigfigs is 4 because 4 is the least number of sig figs. So, when i divide, i get 2019.391672. Since, 3 is the least number of Sigfigs, the answer should be 2.02 x 10^3.

BUT, the answer key is saying otherwise! What am i doing wrong? Am i using the rules right?

 

[fresh_42]

Homework Statement

)(9.66x10^-1) + (5.1x10^2) -8.77+2.8 ) / ((8.333x10^-2)(3.001))

Homework Equations

None

The Attempt at a Solution

my answer does not match the answer key which is 2.0 x 10^3.[/B]
When i did the problem , i ended up get 3 SF answer. The numerator simplies to 504.996 where the sigfigs should be 3 because 0 is the least number of decimals. The denominator is simplified to 0.25007333 where the sigfigs is 4 because 4 is the least number of sig figs. So, when i divide, i get 2019.391672. Since, 3 is the least number of Sigfigs, the answer should be 2.02 x 10^3.

BUT, the answer key is saying otherwise! What am i doing wrong? Am i using the rules right?

I get $2020$ even without calculator, so if I was asked, I'd, too, answered $2.02 \cdot 10^{3}$:
$$((9.66x10^-1) + (5.1x10^2) -8.77+2.8 ) / ((8.333x10^-2)(3.001)) = (1 + 510 -8 +2 )/ (\frac{25}{3}\cdot 3 \cdot \frac{1}{100}) = 505/(\frac{1}{4}) = 2020$$
However, we don't have information about the accuracy of the single numbers, so their uncertainty could lead to only one significant digit. With three it should be $2.02$.

 

[I like Serena]

Hey Lori :)

Doesn't 5.1x10² have 2 significant digits?
After the additions and subtractions, it dominates the other terms in the numerator.
That makes the suggested rounding 2.0x10³.
What does the answer key say?