1. Precision and accuracy in measurements Shows accuracy, but not precision Shows precision but not accuracy

2. Label each experiment. Indicate whether the diagram illustrates precision, accuracy, both, or neither.

3. Accuracy and Precision in measurement Accuracy refers to the agreement of a particular value or measurement with the true or accepted value.Accuracy refers to the agreement of a particular value or measurement with the true or accepted value. Precision refers to how close the values or measurements are to each other.Precision refers to how close the values or measurements are to each other.

4. Uncertainty in Measurement A digit that must be estimated is called uncertain. A measurement always has some degree of uncertainty. When you measure any quantity, the last digit is estimated. In science, you MUST always estimate the last digit. This is called reading to the “precision of the instrument”.

5. STEPS TO READING AN INSTRUMENT CORRECTLY 1.Determine the value of the markings on the instrument 2.Read correctly to that mark. 3.Then estimate the next number. If a measurement falls right on a marking, you MUST estimate the next digit as “ZERO”. 4.Remember!!!!! Your measurement MUST always include an estimated digit.

6. Reading graduated cylinders (read the bottom of the meniscus) 100 mL graduated cylinder

7. Try Again 25 mL graduated cylinder

8. How long is the green line?

9. 060 50 4030 20 10 70 0 100 200 300 0 1 2 345 67

10. 90 80 70 60 50 40 0 10 20 30 40 50

11. http://antoine.frostburg.edu/cgi- bin/senese/tutorials/sigfig/index.cgihttp://antoine.frostburg.edu/cgi- bin/senese/tutorials/sigfig/index.cgi

12. COUNTING SIG. DIGS. WHAT EVERYONE SHOULD KNOW

13. Rules for Counting Significant Figures - Overview 1.Nonzero integers 2.Zeros leading zerosleading zeros captive zeroscaptive zeros trailing zerostrailing zeros 3.Counting numbers 4.Equivilancies

14. NON-ZERO NUMBERS ARE ALWAYS SIGNIFIGANT 45.336 g 5 25.3 mL 3 45 cm 2 12922 cal 5

15. CAPTIVE ZEROS BETWEEN NON-ZERO NUMBERS ARE ALWAYS SIGNIFICANT 25.03 g4 25,001 m5 145.06 kg 5 5.04 m 3

16. LEADING ZEROS IN FRONT OF NON-ZERO NUMBERS ARE NEVER SIGNIFICANT Start counting at the 1 st NONZERO number 0.0025 g 2 0.235 mL 3 0.0003 cm 1 0.000007631 mm 4

17. TRAILING ZEROS COME AFTER NON-ZERO DIGITS ARE SIGNIFICANT IF THERE IS A DECIMAL POINT IN THE NUMBER 25,000 kg 2 25,000.00 g 7 2100 mL 2 57.0 m 3

18. COUNTING NUMBERS ARE INFINITELY SIGNIFICANT WILL NEVER DETERMINE SIG. DIGS. IN ANSWERS 2 sheets of paper 10 pennies There are 26 students in my class.

19. EQUIVILANCIES MEASUREMENTS THAT ARE EQUAL TO EACH OTHER 1 cm = 10 mm 1000 g = 1kg 1 L = 1000 mL 1.00 meters = 100.cm ARE INFINITELY SIGNIFICANT ARE NOT USED TO DETERMINE SIG. DIGS. IN ANSWER

20. Fill in Significant digit practice

21. ExampleSignificant Figures Give the number of significant figures for each of the following. a. A student’s extraction procedure on tea yields 0.0105 g of caffeine. b. A chemist records a mass of 0.050080 g in an analysis. c. In an experiment, a span of time is determined to be 8.050 x 10 -3 s.

22. Significant digits worksheet Chemistry I This worksheet is divided into several parts. Your instructor will assign certain sections as homework. Counting significant digits a. 3.977 g __4__Rule:_Nonzero integers are always significant b. 0.0033 cm__2__ Rule:_Leading zeros are never significant c. 10045 cal__5___Rule:_Captive zeros are always significant d. 14.0 0 C _3____Rule:_Trailing zeros are significant if there is a decimal point e. 1200 mL__2___Rule:_Trailing zeros are not significant if there is not a decimal point

23. Page 53 #4 Student 1 Student 2 Student 3 Trial 1 2.60cm 2.70cm 2.75cm Trial 2 2.72cm 2.69cm 2.74cm Trial 3 2.65cm 2.71cm 2.64cm Average 2.66cm 2.70cm 2.71cm Correct answer is (a.) Student 2 is both precise and accurate

24. Nature of Measurement Measurement - quantitative observation consisting of 2 partsMeasurement - quantitative observation consisting of 2 parts Part 1 – number Part 1 – number Part 2 - scale (unit) Part 2 - scale (unit) Examples:Examples: 20 grams 6.63    Joule· seconds

25. Part 1: Rules for Significant Figures in Mathematical Operations Addition and Subtraction: # sig figs in the answer equals the number of decimal places in the least precise measurement (one with least number of decimal places to the right of the decimal point) 6.8 cm 6.8 cm + 11.934 cm 18.734 cm  18.7 cm (3 sig figs) 18.734 cm  18.7 cm (3 sig figs)

26. Rules for Significant Figures in Mathematical Operations Multiplication and Division: # sig digits in the answer are equal to the measurement with the least number of sig digits used in the calculation. 6.38 cm  2.0 cm = 12.76 cm 2  13 cm 2 (2 sig figs) 6.38 cm  2.0 cm = 12.76 cm 2  13 cm 2 (2 sig figs) 4.92 cm = 1.64  1.6 (2 sig figs) 4.92 cm = 1.64  1.6 (2 sig figs) 3.0 cm 3.0 cm

27. UNITS ON ANSWERS Units in the answer are derived from units in the problem When adding or subtracting, the unit is the same as in the problem. Multiplying like units gives a square measurement (2 cm x 2 cm = 4 cm 2 ) OR a cubic measurement (2 cm x 2 cm x 2 cm = 8 cm 3 ) Multiplying unlike units means that both units appear in the answer separated by a 22.4 L x 1.00 atm = 22.4 L atm

28. Dividing like units cancels the unit--------- 2 cm 2 cm = 1 If you divide unlike units all units MUST appear in the answer. 8.0 g = 2.0 g/mL 4.0 mL (22.4 L)(1.00 atm) = 0.0891L atm (273 K)(1.00 mol) K mol

29. MIXED OPERATIONS Sometimes a calculation involves addition/subtraction AND multiplication/division. Then 2 roundings must take place because there are 2 different rules. 25.0 mL – 15.0 mL = 5 2 mL First : 25.0 mL – 15.0 mL = 10.0 mL then : 10.0mL = 5 (no units) 2 mL

30. APPLYING ROUNDING RULES If the digit to the right of the last sig. digit is < 5, do not change the last sig. digit 2.532  2.53 If the digit to the right of the last sig. digit is > than or = to 5, round up. 2.535  2.54 If the digits to the right of the last sig. digit are 49 you only look at the 4 and do not change the last sig. digit. 2.5349  2.53

31. More Rounding Info 123.456 ones 123.456 tens 123.456 tenths 123.456 hundredths 123.456 thousandths

32. Sig. Digit WS II ( 3 sig. digits) a) 0.02443 kcal = 0.0244 kcal b) 95.56 g = 95.6g c) 57.048 m = 57.0 m d) 12.17 C = 12.2 C e) 1764.9 ml = 1760 ml f) 8.859 km = 8.86 km g) 45,560 mm = 45,600 mm

33. Sig. Digit WS III & IV A e) 43.13g = 43.1g (tenths) f) 155 m = 160 m ( tens) g) 8.859 km = 8.86 km (hundredths) h) 124.78 g = 125 g (ones). 67.14 kg + 8.2 kg = 75.3 kg 87.3 cm - 1.655 cm = 85.6 cm 8.2 cm - 7.11 cm = 1.1 cm 0.042g - 0.02g m = 0.02 g 853.2 mL + 627.443 mL = 1480.6 mL 12.2 0 C + 18.54 0 C = 30.7 0 C