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

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

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.

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”.

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.

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

Try Again 25 mL graduated cylinder

How long is the green line?

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

COUNTING SIG. DIGS. WHAT EVERYONE SHOULD KNOW

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

NON-ZERO NUMBERS ARE ALWAYS SIGNIFIGANT g mL 3 45 cm cal 5

CAPTIVE ZEROS BETWEEN NON-ZERO NUMBERS ARE ALWAYS SIGNIFICANT g4 25,001 m kg m 3

LEADING ZEROS IN FRONT OF NON-ZERO NUMBERS ARE NEVER SIGNIFICANT Start counting at the 1 st NONZERO number g mL cm mm 4

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

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.

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

Fill in Significant digit practice

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

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

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

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

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 cm cm  18.7 cm (3 sig figs) cm  18.7 cm (3 sig figs)

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 cm  2.0 cm = cm 2  13 cm 2 (2 sig figs) 6.38 cm  2.0 cm = 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

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

Dividing like units cancels the unit 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) = L atm (273 K)(1.00 mol) K mol

MIXED OPERATIONS Sometimes a calculation involves addition/subtraction AND multiplication/division. Then 2 roundings must take place because there are 2 different rules 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

APPLYING ROUNDING RULES If the digit to the right of the last sig. digit is < 5, do not change the last sig. digit  2.53 If the digit to the right of the last sig. digit is > than or = to 5, round up  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  2.53

More Rounding Info ones tens tenths hundredths thousandths

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

Sig. Digit WS III & IV A e) 43.13g = 43.1g (tenths) f) 155 m = 160 m ( tens) g) km = 8.86 km (hundredths) h) g = 125 g (ones) kg kg = 75.3 kg 87.3 cm cm = 85.6 cm 8.2 cm cm = 1.1 cm 0.042g g m = 0.02 g mL mL = mL C C = C