measurement accuracy vs precision percent error significant figures scientific notation temperature...
TRANSCRIPT
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 g
18.06 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
E. 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
E. Temperature
• Convert these temperatures:
1) 25oC = ______________K
2) -15oF = ______________ K
3) 315K = ______________ oC
4) 288K = ______________ oF
298.15
298
41.85
298
F. Dimensional Analysis
• Dimensional Analysis is also called Unit Analysis and is a great way to solve problems in chemistry (or any time).
F. 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
F. Dimensional Analysis Problem-Solving Steps
1. Analyze
2. Plan
3. Compute
4. Evaluate
3
3
cm
gcm
F. Dimensional Analysis
• The “Factor-Label” Method– Units, or “labels” are canceled, or “factored” out
g
F. 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.
G. 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
By using dimensional analysis / factor-label method, the UNITS ensure that you have the conversion right side up, and the UNITS are calculated as well as the
numbers!
2.5 hr
1 x 60 min
1 hr = 150 min
G. Conversion FactorsWrite conversion factors that relate each of the following pairs of units:
1. Liters and mL2. Hours and minutes
3. Meters and kilometers
1 L1000 mL
1 hr60 min
1000 m1 km
1000 mL1 L
=
H. 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.
H. 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
H. 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
H. 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
H. SI Prefix Conversions
5) 400. g = ______________ kg
6) 57 Mm = ______________ nm
Dimensional Analysis Practice
1. You have $7.25 in your pocket in quarters. How many quarters do you have?
2. How many seconds are in 1.4 days?
Plan: days hr min seconds
3. How many milliliters are in 1.00 quart of milk?
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?
6. Milton football needs 5.5 yards for a 1st down. How many cm is this?
7. A piece of wire is 1.3 m long. How many 1.5-cm pieces can be cut from this wire?
8. How many liters of water would fill a container that measures 75.0 in3?