This is my exam question The SEmean tells you the accuracy w

This is my exam question: The SE_mean tells you the accuracy with which you estimated the mean number of bacteria per square. Use this estimate to deccide the correct number of significant digits (all digits including the frist for which you are uncertain) by comparing the estimated mean plus the SE_mean and with the estimated mean minus SE_mean. For instance, if the mean is 1234.567 and SE_mean is 98.765, you will have to compare 1234.567 + 98.765 = 1333.332 with 1234.567-98.765 = 1135.802. In this case there are 2 significant digits and the mean should be reported as 1.2 x 10³.

My question: how do we know that there are 2 sig. digits from the SE_mean shown above? Please answer it thoroughly.

Solution

The number of significant digits is the number of digis you are certain.

Note that the uncertainty is 98.765, which means that the uncertain digits start with the tens digit (as the highest place value here is the tens digit, 9).

Thus, only the thousands and hundreds digit are \"certain\", so we have TWO SIGNIFICANT DIGITS. [ANSWER, 2 SIGNIFICANT DIGITS]