+ Accuracy and Precision Accuracy – how close a measured value is to the actual (true) value...

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+ Accuracy and Precision Accuracy – how close a measured value is to the actual (true) value Precision – how close the measured values are to each other Low Accuracy Low Precision Low Accuracy High Precision High Accuracy High Precision

Transcript of + Accuracy and Precision Accuracy – how close a measured value is to the actual (true) value...

Page 1: + Accuracy and Precision Accuracy – how close a measured value is to the actual (true) value Precision – how close the measured values are to each other.

+Accuracy and Precision Accuracy – how close a measured value is to the

actual (true) value

  Precision – how close the measured values are to

each other

Low AccuracyLow Precision

Low AccuracyHigh Precision

High AccuracyHigh Precision

Page 2: + Accuracy and Precision Accuracy – how close a measured value is to the actual (true) value Precision – how close the measured values are to each other.

+Types of Error

Random Error – when you estimate a value to obtain the last sig fig for any measurement Ex. Measuring the temperature to 1 decimal

place using a thermometer

Systematic Error – happens due to an inherent error in the measuring system. Ex. using a worn metre stick to measure

your height

 

Page 3: + Accuracy and Precision Accuracy – how close a measured value is to the actual (true) value Precision – how close the measured values are to each other.

+Significant Figures

Significant figures : the “important” digits in a numerical value.

the number contains all the digits that are certain plus one digit that is uncertain.

 Example: When a measurement is reported to be 47.5, that means the 4 and 7 are the certain numbers and the 5 is the uncertain numbers. It means that the actual value could be any number between 47.4 – 47.6.

Page 4: + Accuracy and Precision Accuracy – how close a measured value is to the actual (true) value Precision – how close the measured values are to each other.

+Significant Figure Rules

Page 5: + Accuracy and Precision Accuracy – how close a measured value is to the actual (true) value Precision – how close the measured values are to each other.

+State the number of significant figures in each of the followings: Measurement S.F. Measurement S.F.a. 967 e. 3.254

b. 1.034 f. 9.3

c. 1.010 g. 2.008

d. 5 h. 8.21

Page 6: + Accuracy and Precision Accuracy – how close a measured value is to the actual (true) value Precision – how close the measured values are to each other.

+ Rules for Sig Figs In Mathematical Operations

Multiplying and Dividing Numbers

In a calculation involving multiplication or division, the number of significant digits in an answer should equal the least number of significant digits in any one of the numbers being multiplied or divided.

e.g. 9.0 x 9.0 =8.1 x 101, while 9.0 x 9 and 9 x 9 = 8 x 101

Page 7: + Accuracy and Precision Accuracy – how close a measured value is to the actual (true) value Precision – how close the measured values are to each other.

+Rules for Sig Figs In

Mathematical Operations

Adding and Subtracting Numbers

When quantities are being added or subtracted, the number of decimal places (not significant digits) in the answer should be the same as the least number of decimal places in any of the numbers being added or subtracted.

e.g. 2.0 + 2.03 = 4.0

Page 8: + Accuracy and Precision Accuracy – how close a measured value is to the actual (true) value Precision – how close the measured values are to each other.

+ Rules for Sig Figs In Mathematical Operations

Rounding Rules

1. If the digit after the one you want to keep is greater than 5, then round up. e.g. To obtain 2 sig digs: 3.47 rounds to 3.5; 3.471

rounds to 3.5

2. If the digit after the one you want to keep is less than five, then do nothing. e.g. To obtain 2 sig digs: 3.44 rounds to 3.4; 3.429

rounds to 3.4

3. If the single digit after the one you want is exactly 5, round to the closest even number. e.g. To obtain 2 sig digs: 2.55 is rounded to 2.6; 2.25 is

rounded to 2.2 e.g. BUT, 2.251 is rounded to 2.3

Page 9: + Accuracy and Precision Accuracy – how close a measured value is to the actual (true) value Precision – how close the measured values are to each other.

+ Sig Fig Practice #2

3.24 m x 7.0 m

Calculation Calculator says: Answer

22.68 m2 23 m2

100.0 g ÷ 23.7 cm3 4.219409283 g/cm3 4.22 g/cm3

0.02 cm x 2.371 cm0.04742 cm2 0.05 cm2

710 m ÷ 3.0 s 236.6666667 m/s 2.4 x 102 m/s

1818.2 lb x 3.23 ft 5872.786 lb·ft 5.87 x 103 lb·ft 1.030 g ÷ 2.87 mL 2.9561 g/mL 2.96 g/mL

Page 10: + Accuracy and Precision Accuracy – how close a measured value is to the actual (true) value Precision – how close the measured values are to each other.

+ Sig Fig Practice #3

3.24 m + 7.0 m

Calculation Calculator says: Answer

10.24 m 10.2 m

100.0 g - 23.73 g 76.27 g 76.3 g

0.02 cm + 2.371 cm 2.391 cm 2.39 cm

713.1 L - 3.872 L 709.228 L 709.2 L

1818.2 lb + 3.37 lb 1821.57 lb 1821.6 lb

2.030 mL - 1.870 mL 0.16 mL 0.160 mL

Page 11: + Accuracy and Precision Accuracy – how close a measured value is to the actual (true) value Precision – how close the measured values are to each other.

+Scientific NotationA method used to express really big or really

small numbers. Consist of two parts:

2.34 x 103

The first part of the number indicates the number of significant figures in the value.

The second part of the number DOES NOT count for significant figures.

This number is ALWAYS between 0 and 10

The 2nd part is always 10 raised to an integer exponent

Page 12: + Accuracy and Precision Accuracy – how close a measured value is to the actual (true) value Precision – how close the measured values are to each other.

+ How its Done1. Place the decimal point between the first

and second whole number, and write ‘x 10’ after the number. e.g. For 12345, it becomes 1.2 x 10 e.g. For 0.00012345, it also becomes 1.2 x 10

2. Indicate how many places you moved the decimal by writing an exponent on the number 10.

a) A move to the left means a positive move. e.g. For 12345, it becomes 1.2 x 104

b) A move to the right means a negative move. e.g. For 0.00012345, it becomes 1.2 x 10-4

Page 13: + Accuracy and Precision Accuracy – how close a measured value is to the actual (true) value Precision – how close the measured values are to each other.

+ The Fundamental SI Units In all sciences, calculations are done using SI units (Le

Système International d'Unités).

Page 14: + Accuracy and Precision Accuracy – how close a measured value is to the actual (true) value Precision – how close the measured values are to each other.

+The Fundamental SI Units

Physical Quantity

Name Abbr.

Length meters m

Time second s

Mass kilogram kg

Temperature Kelvin K

Amount of Substance

mole Mol

Electrical Charge

Coulomb C

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+SI Prefixes

The international system of units consists of a set of units together with a set of prefixes.

Prefix Mega Kilo Hecto

Deca base(g, m, L)

Deci Centi Milli Micro

Symbol M k h da d c m

Factor 106 103 102 101 100 = 1 10-1 10-2 10-3 10-6

Page 16: + Accuracy and Precision Accuracy – how close a measured value is to the actual (true) value Precision – how close the measured values are to each other.

+Practice!

Original Convert to… Original Convert to…

a) 3.15 m cm e) 955g kg

b) 20.0Mg mg f) 178mm cm

c) 75.4L ml g) 650cm mm

d)1350mL L h) 88.74ms

s

Page 17: + Accuracy and Precision Accuracy – how close a measured value is to the actual (true) value Precision – how close the measured values are to each other.

+Practice!

Original Convert to… Original Convert to…

a) 3.15 m 315 cm e) 955g 0.955 kg

b) 20.0Mg 2.00 x 1010 mg f) 178mm 17.8 cm

c) 75.4L 0.0754 mL g) 650cm 6500 mmOr 6.50X103 mm

d)1350mL 1.350 L h) 88.74ms

0.08874s

Page 18: + Accuracy and Precision Accuracy – how close a measured value is to the actual (true) value Precision – how close the measured values are to each other.

+Dimensional AnalysisSAMPLE PROBLEMS…

Convert 7 years to seconds. REMEMBER: Set up conversion factors to get

rid of unneeded units, and to obtain needed units!

Conversion can be flipped if needed:60 s1min

= 1min60 s

= 1


ACCURACY AND PRECISION ACCURACY: refers to how close a measured value is to an accepted value PRECISION: refers to how close a series of measurements.

ACCURACY AND PRECISION ACCURACY: refers to how close a measured value is to an accepted value PRECISION: refers to how close a series of measurements.

Measurements: Accuracy, Precision, & Error

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1.07 Accuracy and Precision

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ACCURACY & PRECISION IN MEASUREMENT

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Precision Workholding Technology PPC Series Precision ...Accuracy is the total indicator reading (radial and lateral runout) of a master gage measured 1.00” (25.4mm) from the top

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Measurement and Significant Figures. Precision and Accuracy What is the difference between precision and accuracy in chemical measurements? Accuracy refers.

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Accuracy, Precision & Significant Analysis Figures ......2017/10/29  · Accuracy • Accuracy = the extent to which a measured value agrees with a standard value Accuracy of a device

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Significant Figures Honors Chem section 1.5. Accuracy vs. Precision Accuracy: how close a measured value is to the true value. Precision: the degree of.

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IMPROVING ACCURACY AND PRECISION OF CALCULATED … · IMPROVING ACCURACY AND PRECISION OF CALCULATED PROCESS VARIABLES BY USING DIRECTLY MEASURED NONSUGARS . Jeffrey L. Carlson Gregory

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Accuracy, Precision ppt

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Standards of Measurements. Accuracy and Precision Accuracy – how close a measured value is to the actual value Precision – how close the measured values.

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