http://www.ck12.org Chapter 1. What Is Science?
Adding and Subtracting with Significant Digits
Rule: When adding or subtracting significant numbers, round to the smallest number of places past the decimal, of
the least precise number in the group.
Example 1: 23.56 + 47.0 = 70.56 = 70.6 (least precise measure is the tenths place)
Example 2: 512 + 48.6295 = 560.6295 = 561 (least precise measure is the ones place)
Example 3: 6× 102 − 10. 76 = 589. 24 = 600 (least precisemeasureisthehundreds place)
Consider why this rule is reasonable. In each example, the two numbers being added or subtracted could not have
been measured with the same instrument. The second number in each pair was measured with a tool of greater
precision. A less accurate measurement cannot be made more accurate by the addition or subtraction of a more
accurate number, no more so than a more precise measuring tool can impart greater precision to a less precise
measuring tool. The precision of the sum or difference computation is therefore always determined using the least
precise tool.
Multiplying and Dividing with Significant Digits
Rule: When multiplying and dividing with significant digits, the final result must be rounded to the same number of
significant digits as the number with the minimum number of significant digits.
Example 1: 23.56×47.0 = 1107.32 = 1110 = 1.11× 103 (round to three significant digits)
Example 2: 512×48.6295 = 24898.304 = 24900 = 2.49× 103 (round to three significant digits)
Example 3: (6× 102 )/10.7 = 56.07476636 = 60 = 6× 101 (round to one significant digit)
Consider why this rule is reasonable.
Recall that the last digit in each number is not an exact measure, but an estimate. When multiplying (or dividing),
the uncertainty of the estimated digits affects every digit. This rule ensures that the uncertainty is never greater than
two digits having a direct calculation from an estimated digit.