chapter 3 measurement accuracy vs precision percent error significant figures scientific notation...
TRANSCRIPT
Chapter 3 Measurement• Accuracy vs Precision• Percent Error• Significant Figures• Scientific Notation• Temperature Conversions• Dimensional Analysis• Conversion Factors• SI Conversions
Number vs. Quantity• Quantity - number + unit
UNITS MATTER!!
A. Accuracy vs. Precision• Accuracy - how close a measurement is to the
accepted value
• Precision - how close a series of measurements are to each other
ACCURATE = CORRECT
PRECISE = CONSISTENT
A. Accuracy vs. Precision
B. Percent Error
• Indicates accuracy of a measurement
100accepted
acceptedalexperimenterror %
your value
given value
B. Percent Error• A student determines the density of a substance to
be 1.40 g/mL. Find the % error if the accepted value of the density is 1.36 g/mL.
100g/mL 1.36
g/mL 1.36g/mL 1.40error %
% error = 2.94 %
C. Significant Figures
• Indicate precision of a measurement.
• Recording Sig Figs– Sig figs in a measurement include the known digits
plus a final estimated digit
2.31 cm
C. Significant Figures• Counting Sig Figs
– Digits from 1-9 are always significant– Zeros between two other sig figs are always
significant– One or more additional zeros to the right of both
the decimal place and another sig digit are significant
– Count all numbers EXCEPT:• Leading zeros -- 0.0025• Trailing zeros without
a decimal point -- 2,500
5085
2.60
739
4. 0.080
3. 5,280
2. 402
1. 23.50
C. Significant Figures
Counting Sig Fig Examples
1. 23.50
2. 402
3. 5,280
4. 0.080
4 sig figs
3 sig figs
3 sig figs
2 sig figs
C. Significant Figures
• Calculating with Sig Figs– Multiply/Divide - The # with the fewest sig figs
determines the # of sig figs in the answer
(13.91g/cm3)(23.3cm3) = 324.103g
324 g
4 SF 3 SF3 SF
C. Significant Figures
• Calculating with Sig Figs (con’t)– Add/Subtract - The # with the lowest decimal value
determines the place of the last sig fig in the answer
3.75 mL
+ 4.1 mL
7.85 mL 7.9 mL
3.75 mL
+ 4.1 mL
7.85 mL
C. Significant Figures
• Calculating with Sig Figs (con’t)– Exact Numbers do not limit the # of sig figs in the answer
• Counting numbers: 12 students• Exact conversions: 1 m = 100 cm• “1” in any conversion: 1 in = 2.54 cm
C. Significant Figures
5. (15.30 g) ÷ (6.4 mL)
Practice Problems
= 2.390625 g/mL
18.1 g
6. 18.9 g
- 0.84 g18.06 g
4 SF 2 SF
2.4 g/mL2 SF
D. Scientific Notation
• A way to express any number as a number between 1 and 10 (coefficient) multiplied by 10 raised to a power (exponent)
• Number of carbon atoms in the Hope diamond
• 460,000,000,000,000,000,000,000 atoms
• 4.6 x 1023 atoms
coefficient exponent
D. Scientific Notation
• Converting into Sci. Notation:
– Move decimal until there’s 1 digit to its left. Places moved = exponent
– Large # (>1) positive exponentSmall # (<1) negative exponent
– Only include sig figs – all of them!
65,000 kg 6.5 × 104 kg
D. Scientific Notation
7. 2,400,000 g
8. 0.00256 kg
9. 7.0 10-5 km
10. 6.2 104 mm
Practice Problems
2.4 106 g
2.56 10-3 kg
0.000070 km
62,000 mm
D. Scientific Notation
• Calculating with Sci. Notation
(5.44 × 107 g) ÷ (8.1 × 104 mol) =
5.44EXPEXP
EEEE÷÷
EXPEXP
EEEE ENTERENTER
EXEEXE7 8.1 4
= 671.6049383 = 670 g/mol = 6.7 × 102 g/mol
Type on your calculator:
D. Scientific Notation
11. (4 x 102 cm) x (1 x 108cm)
12. (2.1 x 10-4kg) x (3.3 x 102 kg)
13. (6.25 x 102) ÷ (5.5 x 108)
14. (8.15 x 104) ÷ (4.39 x 101)
15. (6.02 x 1023) ÷ (1.201 x 101)
Practice Problems
4 1010 cm2
6.9 10-2 kg2
1.1 x 10-6
1.86 x 103
5.01 x 1022
A. Temperature• Temperature
– measure of the average KE of the particles in a sample of matter
273.15Kelvin Co
32Fahrenheit Co 5
9
32Celsius Fo 9
5
Temperature
• Convert these temperatures:
1) 25oC = ______________K
2) -15oF = ______________ K
3) 315K = ______________ oC
4) 288K = ______________ oF
298.15
298
41.85
298
Measurement
Dimensional Analysis
A. Problem-Solving Steps
1. Analyze
2. Plan
3. Compute
4. Evaluate
B. Dimensional Analysis
• Dimensional Analysis– A tool often used in science for converting units
within a measurement system
• Conversion Factor– A numerical factor by which a quantity expressed in
one system of units may be converted to another system
3
3
cm
gcm
B. Dimensional Analysis
• The “Factor-Label” Method– Units, or “labels” are canceled, or “factored” out
g
B. Dimensional Analysis
• Steps to solving problems:1. Identify starting & ending units.
2. Line up conversion factors so units cancel.
3. Multiply all top numbers & divide by each bottom number.
4. Check units & answer.
C. Conversion FactorsC. Conversion Factors
Fractions in which the numerator and denominator are EQUAL quantities expressed in different units
Example: 1 in. = 2.54 cm
Factors: 1 in. and 2.54 cm 2.54 cm 1 in.
How many minutes are in 2.5 hours?
Conversion factor
cancel
2.5 hr2.5 hr
1 1
x x 60 min60 min
1 hr
= 150 min
C. Conversion FactorsWrite conversion factors that relate Write conversion factors that relate each of the following pairs of units:each of the following pairs of units:
1. Liters and mL1. Liters and mL
2. Hours and minutes2. Hours and minutes
3. Meters and kilometers3. Meters and kilometers
1 L1000 mL
1 hr60 min
1000 m1 km
1000 mL1 L
=
D. SI Prefix Conversions
1. Memorize the following chart. (next slide)
2. Find the conversion factor(s).
3. Insert the conversion factor(s) to get to the correct units.
4. When converting to or from a base unit, there will only be one step. To convert to or from any other units, there will be two steps.
A. SI Prefix Conversions
mega- M 106
deci- d 10-1
centi- c 10-2
milli- m 10-3
Prefix Symbol Factor
micro- 10-6
nano- n 10-9
kilo- k 103
BASE UNIT --- 100
giga- G 109
deka- da 101
hecto- h 102
tera- T 1012
mo
ve le
ft
mo
ve r
igh
t
D. SI Prefix Conversions
a. cm to m
b. m to µm
c. ns to s
d. kg to g
1 m100 cm
1 m106 µm
1 s109 ns
1 kg1000 g
D. SI Prefix Conversions
4) 805 Tb = ______________ b
805 Tb 1
1012 b
1 Tb
Terabytes bytes
= 805 x 1012 bytes
= 8.05 x 1014 bytes
8.05 x 1014
D. SI Prefix Conversions
5) 400. g = ______________ kg
6) 57 Mm = ______________ nm
E. Dimensional Analysis Practice
1.1. You have $7.25 in your pocket in You have $7.25 in your pocket in quarters. How many quarters do you quarters. How many quarters do you have?have?
E. Dimensional Analysis Practice
2. How many seconds are in 1.4 days?
Plan: days hr min seconds
E. Dimensional Analysis Practice
3. How many milliliters are in 1.00 quart of milk?
E. Dimensional Analysis Practice
4. You have 1.5 pounds of gold. Find its volume in cm3 if the density of gold is 19.3 g/cm3.
5. Your European hairdresser wants to cut your hair 8.0 cm shorter. How many inches will he be cutting off?
E. Dimensional Analysis Practice
6. Milton football needs 550 cm for a 1st down. How many yards is this?
E. Dimensional Analysis Practice
7. A piece of wire is 1.3 m long. How many 1.5-cm pieces can be cut from this wire?
E. Dimensional Analysis Practice
E. Dimensional Analysis Practice
8. How many liters of water would fill a container that measures 75.0 in3?