units of measurement - eagle...
TRANSCRIPT
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
alexperimentacceptederror %
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 1.401.36g/mLerror %
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
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 - 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
224 g
+ 130 g
354 g
3.75 mL
+ 4.1 mL
7.85 mL
224 g
+ 130 g
354 g
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
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 exponent
Small # (<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) =
5.44 EXP
EE ÷
EXP
EE ENTER
EXE 7 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
273Kelvin 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 Factors
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!
How many minutes are in 2.5 hours?
2.5 hr
1
x
60 min
1 hr
= 150 min
Write conversion factors that relate each of the following pairs of units:
1. Liters and mL
2. Hours and minutes
3. 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
t A. 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) = 10 (base) = 101 (base)
1 (base) = 1 (base)
1 d(base) = 0.1 (base) = 10-1 (base)
1 c(base) = 0.01 (base) = 10-2 (base)
1 m (base) = 0.001 (base) = 10-3(base)
1 µ(base) = 0.000 0001 (base) = 10-6(base)
1 n(base) = 0. 000 000 0001 (base) = 10-9(base)
1 p(base) = 0.000 000 000 0001 (base) = 10-12(base)
The
Great
Man
King
Henry
Died
By
Drinking
Chocolate
Milk
Monday
Night
Partying
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
quarters. How many quarters do
you have?
X
E. Dimensional Analysis Practice
7.25 dollars
1 1 dollar
4 quarters
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