Why Do Significant Digits Include Uncertain Numbers?

[Gauss M.D.]

Homework Statement

How many significant digits does the number 3568 +/- 42 have?

Homework Equations

The Attempt at a Solution

The true value is ranging between 3526 and 3610. Why is there two significant digits and not one? I can't even find a specific definition of significant digits anywhere, just random examples.

 

[NihalSh]

The true value is ranging between 3526 and 3610. Why is there two significant digits and not one? I can't even find a specific definition of significant digits anywhere, just random examples.

It's about the places of error, here the error doesn't exist in the thousand's place. Hundred's place is uncertain in spite of the fact that it is significant!
I hope this helps!

Edit: It always helps to write in scientific notation...usually after rounding off its written as:

$(357±4)\times10=(3.57±0.04)\times10^3$

You are mixing up "certain and uncertain digits" with "significant digits"!...Significant digits include all certain digits and one uncertain digit!...Here digit "3" is certain whereas digit "5", "6", "8" are uncertain in 3568 as you already mentioned due to comparatively large error.

Even scientific notation can mislead you if you aren't careful!