Significant Figures The numbers that count

Reporting Measurements in Science Accuracy of measurements depend on two things: The skill of the person measuring The capacity of the measuring equipment Always read to the smallest mark and estimate one digit beyond If smallest mark is in the tenths place then answer should be in the hundredths place

Numbers in Science Two types of numbers Exact: Measured: ABSOLUTELY correct and obtained by counting Have infinite # of sig figs Measured: Obtained by measuring # of sig figs depend on person measuring

Rules for counting Sig figs If the number is NOT a zero, IT IS significant If it is a zero it’s sig only if: It is between two other sig figs Ends a number with a decimal Rules for counting Sig figs These are the basic rules to be followed when estimating Sig Figs

Counting Sig Figs Identify # of Sig figs: 3.57 288 20.8 20.80 0.010 0.01 0.0100 3.20 x 104 If the number is NOT a zero, IT IS significant If it is a zero it’s sig only if: It is between two other sig figs Ends a number with a decimal

Calculating Sig Figs: Addition & Subtraction A calculated number CANNOT contain more sig figs than the measurements used to calculate it round up or down to match measurement with the least number of decimal places Example: 37.24 mL+ 10.3 mL= 47.54mL Answer: 47.5 mL

Calculating Sig Figs: Multiplication & Division A calculated number CANNOT contain more sig figs than the measurements used to calculate it Example: 1.23 cm x 12.34 cm =15.1782 cm2 Answer: 15.2 cm2 Round down or up to match number with the least # of sig figs

Reminders Always report measurements one place past measuring value If using digital equipment report displayed amount (estimation has already been done) 25 dollars is an exact number 3.5 cm is an estimated measured number