Do Now: (3 minutes) 1. What are the definitions of precision and accuracy? 2. Why are precision and accuracy important when making measurements?

Do Now Discussion: Precision: how close a set of measurements are to each other Accuracy: How close an experimental value is to the actual value We need to be accurate in order for our results to be valuable and we need to be precise in order for our results to be valid.

Significant Figures and Rounding (sig figs) CORNELL NOTES 9/28/09

SIGNIFICANT FIGURES The reliable digits in a measurement based on the accuracy of the measuring tool. The number of digits we use when recording a measurement

GENERAL INFO ON SIG FIGS Sig figs give you information on the EXACTNESS of a measurement When measuring, ONLY ONE estimated digit is allowed to be significant Examples: Meter stick Graduated cylinder

RULE #1: Nonzero digits are always significant sig figs sig figs sig figs

Quick Check: Hold up the number of fingers representing the number of significant figures How many significant figures are in the number 3.127? FOUR!

RULE #2: Zeros are weird and come in 3 types TYPE 1: Leading Zeros TYPE 2: Captive Zeros TYPE 3: Trailing Zeros

RULE #2.1 (Leading Zeros): These come before non-zero digits and don’t count. They are only placeholders sig figs sig figs

RULE #2.2 (Captive Zeros): These are between nonzero digits. They always count as sig figs sig figs 230,004 6 sig figs

RULE #2.3 (Trailing Zeros): Zeros at the right end of the number. They are significant only if the numbers has a decimal point. 100 = 1 sig fig 1.00 = 3 sig figs 100. = 3 sig figs

Quick Check: Hold up the number of fingers representing the number of significant figures in the following: 1. How many sig figs in ? THREE! 1. How many sig figs in 230? TWO!

RULE #3: EXACT NUMBERS Exact numbers have an infinite number of significant figures. ◦ Non-measured numbers (things we count, 8 atoms) ◦ Formulas/equations (area = π r 2 ) ◦ Definitions (1m = 100 cm)

Mathematical Operations and SigFigs

Addition & Subtraction The answer must have as many decimal places as the measurement having the least number of decimal places.

AdditionSubtraction

Quick Check: Hold up the number of fingers corresponding to the number of sig figs in the following: = THREE! ≈ 30.0

Multiplication & Division The answer may contain only as many significant digits as the measurement with the least number of significant digits

Multiplication Division 2 sigfigs3 sigfigs2 sigfigs 1 sigfig 4 sigfigs 1 sigfig

Quick Check: Hold up the number of fingers corresponding to the number of sig figs in the following: 6.0 x 8.97 = TWO! ≈ 54

Rules for Rounding Rule 1: If the digit to be removed is less than 5, the preceding digit stays the same; if it is equal to or greater than 5, round the preceding digit up = =3.1 Rule 2: In a series of calculations, carry the extra digits through to the final result, THEN round 3.05 x x 3.0 = = 51 NOT 3.1 x 5.6 x 3.0 = = 52

Quick Check: In the following question, use your fingers to represent what the digit will be rounded to. (i.e. if it’s rounded up to 2, hold up 2 fingers) When the is rounded to the first decimal point, what is the answer? 4.5!

Deal of the Week: Every day we will have a “challenge” set of questions to answer in partners If 100% of the students present participate If at least 80% of the class answers ALL questions correctly… NO QUIZ ON FRIDAY! You have 30 seconds to find and sit with a partner!

Challenge Questions: On the small sheet of paper, write your name and your partner’s name, the date and the period. Then answer the following questions on that paper: 1. How many significant figures are in ? 2. How many sig figs are in 5000? 3. What is ? 4. What is 8.97 x 7.124? 5. Why are significant figures important?

Homework Problems Due on Friday! Percent Error: ◦ p.49 # 32, 33, 34 Significant Figures: ◦ p. 51 # 35abd, 36abd ◦ p. 53 # 38, 40 Density: ◦ p. 38 # 1, 3 Dimensional Analysis: ◦ p. 45 # 19