Significant figures

Significant figures: Are the numbers in a measurement that include all of the digits that are known, plus the last digit that is estimated.

Calculating can change the # of significant digits Calculating can change the # of significant digits. The following rules will help you determine how many significant figures a reported measurement has.

Rule #1 Every non zero number is assumed to be significant.

Examples: 98 = 2 significant digits 1234.76 = 6 significant digits .555 = 3 significant digits

Rule #2 Zero’s appearing between non zero numbers are significant.

101 = 3 significant digits 100000.00001 = 11 significant digits Examples: 101 = 3 significant digits 100000.00001 = 11 significant digits .6509 = 4 significant digits

Rule 3 The left most zeros appearing in front of significant digits are not significant. They are considered place holders.

Examples: 000.0055 = 2 significant digits

Rule 4 Zeros at the end of a number that are on the right of any non zero number are always significant, when a decimal is present.

Examples: 0.055500 = 5 significant digits

Rule 5 (an exception to rule 4) Numbers that are to the right of a non zero number where there is no decimal present are not significant. Unless it is stated that the measurement is known precisely.

Examples: 5000 = 1 significant digits 550100 = 4 significant digits (The zero between the 1 and the decimal is significant because it is between the significant zero’s after the decimal.)

Rule 6 You have an unlimited number of significant figs if you : Come up with the number by counting every thing. Are getting the number by converting within a system of measurement.

Examples: I counted 10000 = 5 significant digits There are 1000 meter in 1 Km = 4 significant digits There are 3600 seconds in 1 hour = 4 significant digits

Calculating Significant Digits When multiplying or dividing measurements, the final answer can not have more sig digs than the measurement with the smallest # of significant digs.

Example: 50.0 grams x 3.0 = 150 50.001 grams \ 8.3 = 6.0

Calculating Adding and Subtracting When adding and subtracting, the answer must have the same number of decimal places as the number with the least number of decimal places.

Example: 50 grams + 3.55 grams = 54 grams 50.001 grams - 8.3 grams = 41.7 grams