+ accuracy and precision accuracy – how close a measured value is to the actual (true) value...
TRANSCRIPT
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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 AccuracyLow Precision
Low AccuracyHigh Precision
High AccuracyHigh Precision
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+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
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+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.
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+Significant Figure Rules
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+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
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+ 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
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+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
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+ 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
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+ 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
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+ 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
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+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
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+ 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
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+ The Fundamental SI Units In all sciences, calculations are done using SI units (Le
Système International d'Unités).
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+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
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+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
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+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
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+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