[blazerqb14]

I'm taking a Chemistry class online, and my teacher doesn't communicate very well, so I need a second opinion. 

This is the definition for significant figures from my textbook word for word: Significant figures are the digits in any measurement that are known with certainty plus one digit that is uncertain.  Just for clarification, the uncertain digit comes from estimation, as most people here I'm sure would already know

Based on this, if you take a reading from a balance that has an accuracy of 0.01, what is the correct number of decimal places. e.g. 12.1, 12.11, 12.111, or 12.1111 etc?

[rabolisk]

If you are talking about a digital balance, then it would be 12.10 ± 0.05. If you're reading from an analog balance in which you can estimate between 0 and 0.1, then it would be 12.1x ± 0.05.

[blazerqb14]

If you are talking about a digital balance, then it would be 12.10 ± 0.05. If you're reading from an analog balance in which you can estimate between 0 and 0.1, then it would be 12.1x ± 0.05.

What I mean is an analog scale (digital scales were not discussed in the textbook) with marks every 0.01 g such as the picture following.  The way I interpret the text is that I take all the digits known for certain, which results in a reading of something like 12.11, because it is know for certain that the reading is between 12.11 and 12.12, and estimate one digit, giving you 12.11x.

Why do you have your x in the hundredths place when that digit is know for certain?

[Vidya]

In significant figures only last digit is uncertain
if the accuracy is upto 0.01 it means it can measure accurately 100th place and  with uncertainty for the last place digit
 
hence reading can be expressed upto two places of decimals very accurately in which only last digit is uncertain .
12.11 is the correct answer

[blazerqb14]

In significant figures only last digit is uncertain
if the accuracy is upto 0.01 it means it can measure accurately 100th place and  with uncertainty for the last place digit
 
hence reading can be expressed upto two places of decimals very accurately in which only last digit is uncertain .
12.11 is the correct answer

But as you said, the hundredths place is accurate.  Therefore there is no estimated digit in the figure 12.11, right?  If you take a reading of the red dash in the picture below you can see that the measurement is 12.11 < m < 12.12, with no uncertainty.  The only numbers that are between 12.11 and 12.12 are of the form 12.11x, with the digits being aa.aau.