Transcript Measurement/Calculation

Measurement/Calculation
Units of Measure
Metric System
• based on powers of ten, so it’s easy to
convert between units.
• Remember:
– KING HENRY DANCED BEFORE DAWN
COUNTING MONEY
– Or
– KING HENRY DIED BY DRINKING
CHOCOLATE MILK
Units
Mega
kilo
hecto
deka
BASE
deci
centi
milli
M
k
h
da
(none)
d
c
m
103
102
101
100 or
1
10-1
10-2
10-3
106
105
104
micro

10-4
10-5 10-6
How to use
Kilo
Hecto
Deka
BASE
Deci
Centi
Milli
Examples
Kilo
Hecto
Deka
BASE
Deci
Centi
Milli
•
•
•
•
•
20 000
20 L= _______ mL
7 kg
= _______ mg 7 000 000
90 mm = _______ cm 9.0
223 mL = ________ L 0.223
0.49 hm = ______ m 49
SI base units
Quantity
Base Unit
Symbol
Time
second
s
Length
meter
m
Mass
kilogram
kg
Temperature
Kelvin
K
Amount of a substance
mole
mol
SI derived units
(derived units are calculated from base units)
Quantity
Derived Unit
Symbol
Volume: various formulas,
such as LxWxH
cubic centimeters or milliliters
liters
cm3 or mL
L
Density: mass divided by
volume
grams per milliliter or grams per cubic
centimeter
g/mL or g/cm3
NOTE:
• 1 cm3 IS EQUAL TO 1 mL!!!
• And a cc is the same as a cm3
Measurement/Calculation
Scientific Notation/Accuracy
&Precision
Rules to putting into Sci Not
• Must have a whole number between 1- 9
• If you move:
– Decimal to Left…exponent is Positive
– Decimal to Right...exponent is Negative
Examples
• .0032
• 15 300 000
3.2 X 10-3
1.53 X 107
Examples
• 5.00 X 104
50 000
5.00 0 0
• 2.32 X10-3
0 0 2.32
.00232
Addition/Subtraction
• Make exponents the same by moving decimal
place and changing exponent
• Then add/subtract and put in correct Sci Not
OR
Type into your
calculator
Change mode
to Sci
Example
104
5.00 X
+ 2.44 X 103

5.244X 104
OR
EXP
5.00 EE
5.00 X 104
+ .244 X 104
Type into your
calculator
4
+
EXP
2.44 EE
3
Enter
Multiplication/Division
• Multiplication
– Multiply numbers
– Add exponents
• Division
– Divide numbers
– Subtract exponents
• Then put back in correct scientific
notation!
Example
(5.44 × 107 g) ÷ (8.1 × 104 mol) =
=0.67
= 6.7 × 102 g/mol
X 103 g/mol
Type on your calculator:
5.44
EXP
EE
7
÷
8.1
EXP
EE
4
EXE
ENTER
= 671.6049383 = 670 g/mol = 6.7 × 102 g/mol
Accuracy and Precision
• Accuracy: how close a measurement is
to the true value (the “correct answer”)
• Precision: how close a value is to other
values in that series
Are the following groups of measurements
accurate, precise, both, or neither?
1) Given: true mass of sample of zinc is 14.5 g
Measurements made:
13.2 g, 15.6 g, 17.9 g, 12.0 g
2)Given: true volume of sample of water is
33.3mL
Measurements made:
22.4 mL, 22.2 mL, 22.4 mL, 22.3 mL
3) Given: true length of copper wire is 58.5 cm
Measurements made:
58.4 cm, 58.5 cm, 58.5 cm, 58.4 cm
Qualitative: a descriptive measurement
(quality); does not involve numbers
Quantitative:
(quantity)
a numerical measurement
Measurement/Calculation
Significant Figures
Rules to Significant Figures
• If it’s not 0, it counts.
• Example
• 743.44
2
• 24
5
Rules to Significant Figures
•
•
0’s in between significant figures count.
Example
•
•
3
506
20405 5
• .707
3
Rules to Significant Figures
•
All 0’s at the end past the decimal point
count.
Example
•
•
•
2.440 4
784.30 5
Rules to Significant Figures
•
•
0’s as placeholders don’t count.
Example
•
•
440
0.09
2
1
Alternative Way
Pacific
Atlantic
(Present)
(Absent)
Pacific
Atlantic
(Present)
(Absent)
• If the decimal is present, start on the
Pacific side at the first nonzero digit and
count it and all the digits to the right of it.
• If the decimal is absent, start on the
Atlantic side at the first nonzero digit and
count it and all the digits to the left of it.
Adding/Subtracting
•
•
•
Add/Subtract First
The answer has only as many decimal
places as the measurement having the
least number of decimal places.
Example
190.2 g
65.291 g
12.38 g
267.871 g
1
3
2
Answer should have 1
decimal place
267.9 g
Multiplication/Division
Mult/Divide First
•
•
The answer has only as many
significant figures as the measurement
with the least number of significant
figures.
Example
13.78 g
11.3 mL
4
3
= 1.219469 g/mL
1.22 g\ml
Answer should have 3
significant figures
•
Example
– 15000
2
– 2030.0
5
– 0.0020
2
Measurement/Calculation
Density
Density
• Derived unit
– g/mL or g/cm3
• Mass/Volume
m
D
V
D. Density
• An object has a volume of 825 cm3 and a
density of 13.6 g/cm3. Find its mass.
GIVEN:
WORK:
V = 825 cm3
D = 13.6 g/cm3
m=?
m = DV
m
D
V
m = (13.6 g/cm3)(825cm3)
m = 11 220 g=11 200g
D. Density
• A liquid has a density of 0.87 g/mL. What
volume is occupied by 25 g of the liquid?
GIVEN:
WORK:
D = 0.87 g/mL
V=?
m = 25 g
V=m
D
m
D
V
V=
25 g
0.87 g/mL
V = 28.74mL = 29 mL
D. Density
1. A marble has a mass of 5.6 g. It is placed
in a graduated cylinder with 50.0 mL of
water. The water level rises to 53.4 mL.
What is the density of the marble? 3.4 mL
GIVEN:
WORK:
D=?
V = 53.4-50 =3.4 mL
m = 5.6 g
m
D
V
D=m
V
D=
5.6 g
3.4 mL
D=1.647 g/mL = 1.6 g/mL
Graphing
Graphing is an important tool for expressing data so that it is easier to read
and interpret
Rules for graphing:
--place the manipulated/independent variable (the one that was changed)
on the x axis.
--place the dependent/responding variable (the results of that change) on
the y axis.
(dry mix)
DRY
MIX
y scale = largest y value – smallest y value
# of lines on the y axis
The graph should cover at least ¾ of the grid
x scale = largest x value – smallest x value
# of lines on the x axis