Physics
Vandebilt Catholic High School
Walt Dupre

1. Because the precision of all measuring devices is limited, the number of digits that can be assumed for any measurement is also limited.
    
1. Significant digits (figures) are all the numbers that can be read directly from a measuring device plus one final digit that is estimated (guessed at). Therefore the last digit in a measurement is uncertain. In order to eliminate as much error as possible it is essential to have only one uncertain digit for each measurement taken.
2. Significant digits are only important when taking measurements; significant digits are of no consequences when counting or sequencing items. Measurements should be read to one more decimal place than the smallest scale division of the measuring instrument. This last decimal place is the uncertain digit.
3. Likewise, significant digits have nothing to do decimal places.
4. To insure that the most meaningful answers are obtained, rules for significant digits should be followed throughout this course.
2. Textbook rules for determining significant digits.
1. All non-zeros are significant
2. Zeros between two non-zeros are significant
3. Zeros in front of the first non-zero digit are NOT significant
4. Zeros behind the last non-zero digit are significant ONLY if the number contains a decimal. If there is no decimal point, then these trailing zeros are NOT significant.
5. The entire coefficient of numbers in proper scientific notation is significant.
6. Examples:

Measurement	Significant Digits
123 cm	3
1001 m	4
0.00012 kg	2
2100 cg	2
2.00 X 102 mm	3

3. My rules for determining the number of significant digits.
1. Count the number of significant digits from left right.
2. If the number has a decimal, begin counting with the first non-zero digit and count ALL digits that follow.
3. If there is no decimal, begin counting with the first non-zero digit and stop counting at the last non-zero digit.
4. Mathematical operations with significant digits
1. The results of any mathematical operation with measured quantities cannot be more precise than the least precise quantity used in the calculation. Remember that significant digits are only considered with measurements. Do not consider significant digits with numbers that were strictly for counting purposes.
2. After adding or subtracting round off the answer to agree in precision with the least precise value used in the calculation. That is, the answer must have the same number of decimal places as the number with the smallest number of decimal places used in the calculation.

                23.01 cm + 4.2 cm = 27.2 cm

3. After multiplying or dividing round off the answer to the same number of significant digits as the quantity with the least number of significant digits used in the calculation.

                 3.5 cm X 6.1 cm = 21. cm²

4. Remember the final answer must contain only 1 uncertain digit.
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