Question

What is 34,696 to 2 significant figures?

Answer 1

Heres a trick a friend of mine taught me,
When trying to find the number of sig. figs. in a number, first check for a decimal point.
If there is not a decimal point (as in this case) then count each digit from right to left, starting at the first non-zero digit.
Example 1: 34,696 it would be 5 significant figures (6, 9, 6, 4, 3)
Example 2: 34,600 would be 3 sig figs (6, 4, 3), the two 0's in this number do not count as sig figs.

If there IS a decimal point, then count from left to right starting from the first non-zero digit.
Example 1: 0.0001 would be one significant figure (1)
Example 2: 1.02345 would be six sig figs, (1, 0, 2, 3, 4, 5)

Now back to the actual question...
If you were to estimate 34,696 to 2 sig figs, then according the the rules of estimating, because the '6' in the hundreds place is greater or equal to 5, the next digit (in the thousands place) must have one added to it.
So 35,000 would be the proper way to round 34,696.

How to check: Count from left to right, the first non-zero digit is 5, so (5, 3).

Hope this helps! :D