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General Rules
The three general rules for working with significant figures are that leading zeros are never significant, embedded zeros (e.g., 101) are always significant and trailing zeros are significant only when a decimal point is specified.
Recording Data to the Correct Number of Significant Figures
To use significant figures appropriately, write measured values to the same number of digits that you measure. For example, if you measure a length of rope with a ruler and find that the rope is exactly 10 cm long and the smallest subdivision of the ruler is 0.1 cm, write the length of the rope as "10.0 cm." The number of significant figures represents the precision of your measurement. Do not write "10 cm" because this implies a lower precision than your measurement, and do not write "10.00 cm" because this implies a higher precision.
Rules for Rounding
If the digit to be removed is greater than five, the last remaining digit is rounded up and increased by one. If the digit to be removed is less than five, the remaining digit is rounded down and decreased by one.
However, if the remaining digit is five, the next digit must be considered. If it is not a zero, round it up. Otherwise, round the number up if the last non-zero digit is odd or round it down if it is even.
Adding and Subtracting
When adding and subtracting numbers that have the same number of significant figures, use the same number of significant figures for the answer as in the two numbers you are adding or subtracting. For example, 8.12 + 2.10 = 10.2, not 10.22 or 10.220.
For all other cases where the numbers have differing numbers of significant figures, the rule is that the number with the largest decimal place and fewest significant figures determines the number of significant figures used in the answer. For example, 4.0 - 2 = 2 and 9 - 0.1 = 9, not 2.0 and 8.9 respectively because these answers imply greater precision than what is really known.
Multiplying and Dividing
If you are multiplying or dividing two numbers, the number with the fewest number of significant figures determines the number of significant figures in the answer. If you are multiplying or dividing two numbers with the same number of significant figures, the number of significant figures in the answer is the same. For example, 4.8 * 7.0 = 34, 4.0 * 3.0 = 12 and 8.0 / 2.0 = 4.0. Some examples of the rule when the two numbers have different numbers of significant figures are 5.97 * 2.0 = 12, 200.0 / 6 = 33.33 and 78.0 * 0.001 = 0.08.