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 Accuracy refers to the agreement of a refers to the agreement of a particular value or measurement with particular value or measurement with thethe true true or acceptedor accepted value.value.

• PrecisionPrecision refers to how close the values refers to how close the values or measurements are to each other.or measurements are to each other.

Uncertainty in Measurement

A digit that must be A digit that must be estimatedestimated is called is called uncertainuncertain. A . A measurementmeasurement always always has some degree of uncertainty. has some degree of uncertainty. When you measure any quantity, the When you measure any quantity, the last digit is estimated . In science, you last digit is estimated . In science, you MUST always estimate the last digit. MUST always estimate the last digit. This is called reading to the “This is called reading to the “precision precision of the instrument”.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 Again25 mL graduated cylinder

How long is the green line?

0 605040302010 70

0 100 200 300

0 1 2 3 4 5 6 7

90

80

70

60

50

40 0

10

20

30

40

50

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

COUNTING SIG. DIGS.

WHAT EVERYONE SHOULD KNOW

Rules for Counting Significant Figures - Overview

1.1. Nonzero integersNonzero integers

2.2. ZerosZeros• leading zerosleading zeros

• captive zeroscaptive zeros

• trailing zerostrailing zeros

3.3. Counting numbersCounting numbers

4.4. EquivilanciesEquivilancies

NON-ZERO NUMBERS

• ARE ALWAYS SIGNIFIGANT

• 45.336 g 5

• 25.3 mL 3

• 45 cm 2

• 12922 cal 5

CAPTIVE ZEROS

• BETWEEN NON-ZERO NUMBERS

• ARE ALWAYS SIGNIFICANT

• 25.03 g 4

• 25,001 m 5

• 145.06 kg 5

• 5.04 m 3

LEADING ZEROS

• IN FRONT OF NON-ZERO NUMBERS• ARE NEVER SIGNIFICANT• Start counting at the 1st NONZERO

number• 0.0025 g 2• 0.235 mL 3• 0.0003 cm 1• 0.000007631 mm 4

TRAILING ZEROS

• COME AFTER NON-ZERO DIGITS

• ARE SIGNIFICANT IF THERE IS A DECIMAL POINT IN THE NUMBER

• 25,000 kg 2

• 25,000.00 g 7

• 2100 mL 2

• 57.0 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

Example Significant 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 .

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 0C _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

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• 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

Nature of Measurement

• Measurement - quantitative observation Measurement - quantitative observation consisting of 2 partsconsisting of 2 parts

Part 1Part 1 – number– number

Part 2 - scale (unit)Part 2 - scale (unit)

• Examples:Examples:20 grams20 grams

6.63 6.63 Joule Joule·· seconds seconds

Part 1: Rules for Significant Figures in Mathematical Operations

Addition and SubtractionAddition and Subtraction: : # sig figs in the # sig figs in the answer equals the number of decimal answer equals the number of decimal places in the least precise measurement places in the least precise measurement (one with least number of decimal places (one with least number of decimal places to the right of the decimal point)to the right of the decimal point)

6.8 cm6.8 cm+ + 11.934 cm11.934 cm 18.734 cm 18.734 cm 18.7 18.7 cm (3 sig figs) cm (3 sig figs)

Rules for Significant Figures in Mathematical Operations

Multiplication and DivisionMultiplication and Division: : # sig digits in the answer are # sig digits in the answer are equal to the measurement with the equal to the measurement with the leastleast number of sig number of sig digits used in the calculation.digits used in the calculation.

6.38 cm 6.38 cm 2.02.0 cm = 12.76 cm cm = 12.76 cm22 13 13 cmcm22 (2 sig figs) (2 sig figs)

4.92 cm4.92 cm = 1.64 = 1.64 1.61.6 (2 sig figs) (2 sig figs) 3.03.0 cm 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 cm2 ) OR a cubic measurement (2 cm x 2 cm x 2 cm = 8 cm3)• 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--------- 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

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

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

More Rounding Info• 123.456• ones• 123.456• tens• 123.456• tenths

• 123.456• hundredths

• 123.456• thousandths

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

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 0C + 18.54 0C = 30.7 0C