1. ## Significant Figure

Q) Express 2 344.682 8¸ correct to 3 significant figures.

Options are

(A) 2 344 683
(B) 2 350
(C) 2 340
(D) 235
(E) 234

To me the answer should be 234 which is E but the answer given is 2340 i.g C

Why is it C and why we write 0 after 234.To me it will make 4 significant number.

2. Originally Posted by haftakhan
Q) Express 2 344.682 8¸ correct to 3 significant figures.

Options are

(A) 2 344 683
(B) 2 350
(C) 2 340
(D) 235
(E) 234

To me the answer should be 234 which is E but the answer given is 2340 i.g C

Why is it C and why we write 0 after 234.To me it will make 4 significant number.
Trailing zeros in whole numbers are not significant (why? See my alternative solution for a clue).

If you rounded to the nearest whole number it'd be 2345, which obviously has four significant figures. So you need to round 2 344.682 8 to the nearest decade.

By the way, a rounded answer of 234 does not seem very close to 2345 .... (common sense should always be used to check an answer).

Alternatively: In scientific notation your number can be written 2.3446828 x 10^3. If you only want three significant figures, it becomes 2.34 x 10^3 which can obviously be written as 2340.

3. The point of "significant figures" is to get a number that is still close to the actual number!

2344.6828- 2340= 4.628.

2344.6828- 234= 110.6828- that's not at all close!

Determining whether or not "trailing zeros" are "significant" is a problem. That's why the use of "significant figures" for measurements is almost always allied with "scientific notation".

2344.6828, to 3 significant figures in scientific notation would be $\displaystyle 2.34 \times 10^3$. The number 2340.6838 to 4 significant figures, in "normal" notation would also be 2340 where it is not clear that the final "0" is intended to be significant. In scientific notation, that would be $\displaystyle 2.340 \times 10^3$ which makes it very clear that the last 0 is significant, otherwise, it wouldn't be written.

$\displaystyle 2.34 \times 10^3$ could mean any number from 2335 to 2344. $\displaystyle 2.340 \times 10^3$ could mean any number from 2339.5 to 2340.5.