Clarification on Significant Figures

[Anya Holbrook 1E]

Just to make sure, when determining the number of significant figures zeros would only count if they are not at the end of a decimal correct? For example, 0.034 and 0.304 would both have 3 significant figures while 0.340 would only have two, correct? Thanks!

[jadensteplight_2F]

I could possibly be wrong here, but I think that leading zeros are the zeros that do not count. For instance, 0.034 would have only 2 sig figs, whereas 0.304 would have 3 sig figs since the zero second zero is in the middle and not leading.

However, I am a bit rusty on sig fig rules, so feel free to correct me if I'm wrong here.

[Samiha Molla 3G]

I could possibly be wrong here, but I think that leading zeros are the zeros that do not count. For instance, 0.034 would have only 2 sig figs, whereas 0.304 would have 3 sig figs since the zero second zero is in the middle and not leading.

However, I am a bit rusty on sig fig rules, so feel free to correct me if I'm wrong here.

I think this is correct! leading zeros are not considered significant, while trailing zeroes after a decimal point and those sandwiched between two non-zero digits are.

[Justin Zhang_1A]

So I think zeros to the left of the first non-zero digit are not significant, so 0.034 would only have two sig figs. Trailing zeros in the decimal portion are significant, so 0.340 would have 3 sig figs.

[David Liu 1E]

The person who posted above is right! And I'm also kind of rusty on sig figs but I'm pretty sure 0.340 has 3 sig figs, because the sig fig rule is that trailing zeroes to the right of the decimal are significant, so it should count?

[gabbi_r2C]

Leading zeros in a decimal (zeros after the decimal point and before a digit) do not count for sig figs, ie 0.034 only has 2 sig figs. Zeros between digits (in the case of 0.304, or 102 for a non-decimal number) always count for sig figs. For decimals only, if you add zeros after digits (ie, 0.0340 and 1.0), they count as sig figs. For whole numbers, if they are not followed by a decimal point, they do not count for sig figs (ie, 1020 has 3 sig figs, while 1020. has 4).

[Brianne Conway 1D]

I could possibly be wrong here, but I think that leading zeros are the zeros that do not count. For instance, 0.034 would have only 2 sig figs, whereas 0.304 would have 3 sig figs since the zero second zero is in the middle and not leading.

However, I am a bit rusty on sig fig rules, so feel free to correct me if I'm wrong here.

Yes you're exactly right; leading zeros do not count, while trailing zeros count as long as they are either to the right of the decimal point or the decimal point is shown in the case of a whole number.

[Catie Donohue 2K]

For me, it helps to think about converting the number to scientific notation, because then it's clearer which zeros should be counted.

In your example 0.034, you would move the decimal to the right two places and the two leading zeros would disappear. It would be 3.4E^-2 and it's clearer to see that there are only two sig figs :)

[Javier Perez M 1H]

Hope this helps when it comes to significant figures:
non-0 numbers are considered significant figures
numbers including zeros in between non zero numbers ae considered significant figures as well
Zeros in front, or "leading zeroes" are not counted as significant numbers
Zeros in back, or "trailing zeros" are not considered significant figures if there is no decimal present and if a decimal is present do count them
For more info refer to Khan Academy's video on significant figures

[Juwon Lim 2A]

Leading zeros do not count as significant figures. 0.034 would be 2 sig figs and 0.0034 would still be 2 sig figs. Trailing zeros do not count as significant figures unless there are decimal points. 100 would be 1 sig fig, however 100.00 would be 5 sig figs.
To answer the question, 0.034 would be 2 sig figs, 0.304 would be 3 sig figs, and 0.340 would be 3 sig figs.