Significant Digits

Rules for Significant Digits

Do Not Confuse Significant Digits with Decimal Places

Rule of Thumb: When multiplying or dividing measured numbers, the result should have as many digits as the measured number with the fewest digits.

Example: cm X 0.205cm = ? The measured number with the fewest digits is 0.205cm, so the product should be rounded off to 3 significant digits: 2.15cm 2

Example: 8.500g 4.50cm 3 = ? 8.500g  4.50cm 3 = ? The measured number with the fewest digits is 4.50cm 3, so the quotient should be rounded off to 3 significant digits: 1.89g/cm 3

Sometimes Scientific Notation is Required to Express Products or Quotients in the Correct number of Significant Digits: g 0.5cm 3 = ? g  0.5cm 3 = ? 3 X 10 1 g/cm 3

When numbers are written in scientific notation, the number of significant digits is expressed in the coefficient. Example: 3 X 10 1 g/cm 3 has one significant digit.

Rule for rounding: If a digit is 5 or more round the previous digit up; otherwise leave the previous digit at its value. Examples: Round to 4 significant digits Round to 4 significant digits Round to 4 significant digits

If one is multiplying a measured number by a counting number or π, ignore the digits of the counting number or π. Example: Aluminum rods are 5.6cm long. The total length of 7 rods would be 7 X 5.6cm = 39cm (not 39.2cm). The product would be rounded off to 2 digits as in 5.6cm.

To avoid a rounding off error during multi-step calculations, round off the answer at the end of the calculations not at each intermediate step. Example: A rectangular solid block has a length of 8.89cm, a width of 2.61cm, and a height of 0.61cm. Its mass is 5.329g. Its density would be 5.329g 8.89cm X 2.61cm X 0.61cm) = 5.329g  ( 8.89cm X 2.61cm X 0.61cm) = 5.329g cm 3 = 0.38g/cm g  cm 3 = 0.38g/cm 3 not 5.329g 14cm 3 not 5.329g  14cm 3