Transcript sig. figs.

Measurement and
Units
Chapter 2
SI System
 SI System = metric system
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Used world-wide
Based on powers of 10 (everything is a
factor of 10)
Easy to convert units
SI Base units
 Temperature - Kelvin (K)
 Time - second (s)
 Mass - gram (g)
 Length - meter (m)
 *Volume - Liter (L) (*derived unit)
 These base units can have prefixes
attached to them to give them new
meaning
Metric Prefixes- pg. 33
Prefix
Prefix
Symbol
Multiplier
mega-
M
106 = 1 000 000
kilo-
k
103 = 1 000
BASE UNIT
-
100 = 1
centi-
c
10-2 = 0.01
milli-
m
10-3 = 0.001
micro-
μ
10-6 = 0.000 001
-gram
-meter
-Liter
-second
Powers of 10
A bigger power of 10…
Ex: 109 > 103
Ex: 10-1 > 10-4
…means that there are MORE of the smaller unit
Ex: 103 > 100 = 1000 meters in 1 kilometer
(kilo-) (-meter)
Ex: 100 > 10-3 = 1000 milligrams in 1 gram
(-gram) (milli-)
 Is 5.0 different than 5.00?
Uncertainty in Measurement
 Measuring tools have limits.
 Only the last reported digit is estimated--
everything else is known for certain
 Need to figure out what each marking on the
tool means so you know where to stop reporting
digits
 Accuracy vs. precision
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Accuracy: How close you are to the accepted value
Precision: How close all of your measurements are
to each other
Significant Figures
 Significant Figures (sig. figs.): the number of
digits that carry meaning contributing to the
precision of a measurement or calculated data.
 Include all known digits + one estimated digit
 5.0 cm IS different from 5.00 cm, because you are
able to measure out to different places.
 Affects measurements, rounding, and calculations
Sig Fig rules
 All NON-ZERO digits (1-9) are ALWAYS
significant
 Exact numbers (where there is no uncertainty)
have an INFINITE number of sig figs
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36 inches = 1 yard
100 cm = 1 m
There are 12 oranges
Sig Fig Rules: 0’s
 0’s in the MIDDLE of non-zero digits are
ALWAYS significant
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501.1 cm = 4 sig figs
501.10 cm = 5 sig figs
 0’s at the BEGINNING of a non-zero digit are
NEVER significant
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0.000849 kg = 3 sig figs
0.0008490 kg = 4 sig figs
 0’s at the END of a number are ONLY
significant IF there is a decimal
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849,000 = 3 sig figs
849,000. = 6 sig figs
Sig. Figs. Practice
1)
2)
3)
4)
5)
6)
7)
8)
0.020110 L
730800 kg
48381 m
9807000 mm
0.008401 mL
40.500 s
64000 km
64000.00 km
Rounding Sig. Figs.
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After you determine the amount of sig figs that a
number should have…(based on the type of
calculation…more to come)
 Round to that number of digits without changing
the value of the number too much.
 Ex. 1) 7.867 g to 2 sig figs
 Ex. 2) 89.33 cm to 3 sig figs
 Ex. 3) 89,370. km to 3 sig figs
 Ex. 4) 0.0084386 s to 3 sig figs
Calculations w/Sig Figs
 Add/Subtract:
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Round to the least precise digit.
 Keep
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the fewest number of decimal places
Include units
Example:
28.0 cm + 23.538 cm + 25.68 cm
= 77.218 cm
28.0 cm was the least precise measurement,
so round to 77.2 cm
Example
 4.32 cm – 1 cm
 Answer: 3 cm
Calculations w/Sig Figs
 Multiply/Divide
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Round to the least precise measurement
 Least
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number of sig figs total
Include units
Example:
4,980,000 km x 0.0028 km
= 13,944 km2
…Answer can only have 2 sig figs, so round to
14,000 km2
Example
 364.530 mm / 0.204 s
 Answer: 1790 mm/s
Review rules for calculating
 Adding/subtracting: least number of
decimal places
 Multiplying/dividing: least number of sig
figs
Dimensional Analysis:
 Converting units—2 measurements are
equal to each other, but the units are
different
 Units need to cancel
 Show your work, round for sig figs at the
end
Density
 A physical property of matter
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Can be used to identify unknown elements
 The amount of mass per unit volume
 For solids: g/cm3
 For liquids & gases: g/mL
D = M
V
 If a solid piece of metal has a mass of
13.5 g, and the volume is 5.0 cm3,
calculate the density of the metal.
 If an unknown liquid has a density of
0.998 g/mL, and the mass of the sample
is 2.014 g, calculate the volume of the
sample.