Post on 02-Jan-2016
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
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.
2.94%
100g/mL 1.36
g/mL 1.36g/mL 1.40error %
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
Zeros at the end of a number are significant when a decimal is present
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
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) =
C. Significant Figures
Calculating with Sig Figs (con’t) Add/Subtract – Answer can have as
many # after the decimal as the # with the least amount of # to the right of the decimal
3.75 mL
+ 4.1 mL
7.85 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 answerCounting numbers: 12 studentsExact conversions: 1 m = 100 cm “1” in any conversion: 1 in = 2.54 cm
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
4.6 x 1023
Mass of one carbon atom
0.00000000000000000000002 g
2 x 10-23 g 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
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
A. Temperature
Temperature measure of the average
KE of the particles in a sample of matter
273.15Kelvin Co
32Fahrenheit Co 5
9
32)Celsius F( 9
5 o
Convert these temperatures:
1) 25oC = ______________K
2) -15oF = ______________ K
3) 315K = ______________ oC
4) 288K = ______________ oF
A. Temperature
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.
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.
C. Conversion FactorsC. Conversion Factors
Conversion factor
cancel
By using dimensional analysis / factor-label method, By using dimensional analysis / factor-label method, the UNITS ensure that you have the conversion right the UNITS ensure that you have the conversion right side up, and the UNITS are calculated as well as the side up, and the UNITS are calculated as well as the
numbers!numbers!
How many minutes are in 2.5 hours?
2.5 hr2.5 hr
1 1
x x 60 min60 min
1 hr
= 150 min
Write conversion factors that Write conversion factors that relate each of the following pairs relate each of the following pairs of units:of units:
1. Liters and mL1. Liters and mL
2. Hours and minutes2. Hours and minutes
3. Meters and kilometers3. Meters and kilometers
C. Conversion Factors
Learning Check:
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.
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
tA. SI Prefix Conversions
pico- p 10-12
D. SI Prefix Conversions
1 T(base) = 1 000 000 000 000(base) = 1012 (base)
1 G(base) = 1 000 000 000 (base) = 109 (base)
1 M(base) = 1 000 000 (base) = 106 (base)
1 k(base) = 1 000 (base) = 103 (base)
1 h(base) = 100 (base) = 102 (base)
1 da(base) = 101 (base)
1 (base) = 1 (base)
10 d(base) = 1(base)
100 c(base) = 1 (base)
1000 m (base) = 1(base)
1 (base) = 1 000 000 µ = 10-6(base)
1 (base) = 1 000 000 000 n = 10-9(base)
1 (base) = 1 000 000 000 000 p = 10-12(base)
Tera-
Giga-
Mega-
Kilo-
Hecto-
Deka-
Base
Deci-
Centi-
Milli-
Micro-
Nano-
Pico-
D. SI Prefix Conversions
1) 20 cm = ______________ m
2) 0.032 L = ______________ mL
3) 45 m = ______________ m
You have $7.25 in your pocket in You have $7.25 in your pocket in quarters. How many quarters do quarters. How many quarters do you have?you have?
X
E. Dimensional Analysis Practice
7.25 dollars7.25 dollars
11 1 dollar1 dollar4 quarters4 quarters
How many seconds are in 1.4 days?
= 12000 s
E. Dimensional Analysis Practice
1.4 days
24 hr 60 min
60 s
1 day
1 hr 1 min
You have 1.5 pounds of gold. Find its volume in cm3 if the density of gold is 19.3 g/cm3.
E. Dimensional Analysis Practice
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) Roswell 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