Significant Digits or Significant Figures

WHY??? The number of significant figures in a measurement is equal to the number of digits that are known with some degree of confidence (i.e. our good friends ACCURACY and PRECISION)

What is significant?? In a measurement, such as 3.25, the significant digits include the number of digits that are known with some degree of confidence (3 and 2) plus the last digit (5), which is an estimate or approximation.

Rules for counting Sig Figs Zeros within a number are always significant Both 4308 and 40.05 contain four significant figures Zeros that do nothing but set the decimal point (place holders) are not significant 470,000 and 0.000047 have two significant figures Trailing zeros that aren't needed to hold the decimal point are significant 4.00 and 0.00400 have three significant figures

Practice 12.760 0.00034 9.0034 0.0901 3.8 x 107 1.096 x 10-3 987 600 54 004 -43.803 0.210

Rules for rounding off Imagine that you want to have 2 significant digits…. If the digit after is smaller than 5 (<5), don’t change the digit. Ex: 12. 4  12 If the digit after is > 5, round up. Ex: 12. 6  13 If the digit after is 5… If the digit that you are rounding is even, round down. Ex: 12,5  12 If the digit that you are rounding is odd, round up Ex: 17.5  18

Practice Round off to have 3 significant figures. 1.854 96.019 974 501 273.51 930.8 381.5 0.004 745

What if they’re not all the same?? How do you calculate the significant figures in the answer to an equation where the components have different sig figs? 150.0 + 0.507 0.005580 x 67 4 3 Now what?? 4 2

IMPORTANT When combining measurements with different degrees of accuracy and precision, the accuracy of the final answer can be no greater than the least accurate measurement.

Addition and Subtraction with Significant Figures A simple rule for addition and subtraction: When measurements are added or subtracted, the answer can contain no more decimal places than the least accurate measurement.

Practice 14m/s + 11.8m/s = 0.370m + 0.4876m = 45.23s – 3.8s = 58.035cm + 4.72cm =

Multiplication and Division With Significant Figures A simple rule for multiplication and division: When measurements are multiplied or divided, the answer can contain no more significant figures than the least accurate measurement.

Exceptions!! “Counting” numbers are not used to calculate the number of significant digits Example: If 124.79 grams of candy are to be divided among 4 children, how many grams would each child receive? The number “4” is a counting number. The answer would be given with 5 significant digits 124.79 4 4

Exceptions!! “Constant values” are not used to calculate the number of significant digits Example: How many minutes are there in 2.75 hours? The constant value used in this calculation is 60 minutes/hour, but the number of significant digits in “60” is not counted. The answer would be given with 3 significant digits 2.75