Ch 5: Measurements and
Calculations
I. Scientific Notation and Units
A. Scientific Notation: A way to easily show lengthy
numbers.
1.
Thegrams
Sun isof93,000,000
away if you travelled 5000 miles
per hour
12
carbon hasmiles
602,200,000,000,000,000,000,000
atoms
in it.
n
MIfhow
x
10
where
1
<
M
<
10
many
hours would
take
to reach
sun?
a pile
of carbon
weighsit 41
grams,
howthe
many
carbon atoms are in the pile?
How many days would it take to reach the sun?
different
to show
a number
/ 10years
= way
n = decimals to move.
HowA4.3
many
would
it take
to reachand
the sun?
a) Move
till number is between 1 and 10
x 10decimal
= =
4.3 /10/10
b) Determine
4.3 /10/10/10
x 10 x 10 =the
= exponent (n)
– 4.3
Positive
nx10
=this
moved
to the left
What’s
x 10the
x 10rule
= shows?
time
by 10toitthe
moves
the decimal to the left 1 spot
– Every
Negative
ndivide
–this
moved
right
What’s
theyou
rule
shows?
Every time you multiply by 10 it moves the decimal to the right 1 spot.
Scientific Notation Practice
• Change the following to Scientific Notation
1.
2.
3.
4.
9314
0.08042
0.0000517
7,124,369,582
• Change the following to standard numbers.
1. 4.17 x 104
2. 6.19 x 10 -2
3. 3.001 x 10-5
4. 5.91 x 10 7
B. Units: Indicator of what scale is used for measuring.
1. International System of Measurement (SI)
a.
b.
c.
d.
e.
Mass = The quantity of matter in an object = Grams (g)
Length = Meters (m)
Time = Seconds (sec)
Temperature = Kelvin (K)
Volume = 3 dimensional space taken up = Liter (L)
C. Use prefixes to make numbers usable (verbal
multiplier)
Converting Metric Prefixes.
1. Determine the difference between the
exponent for each unit.
2. Move the decimal that many places.
Base Unit
-g
-L
-m
• If going down the table, move right.
• If going up the table move left.
Convert The following
5.45kg  g
6.19nm  m
100
4.90 x 107 µL  kL
1.34 x 10-5 ML  L
µ
II. Uncertainty in Measurments
A. All measurements have an estimated digit.
1. Determine the smallest digit that is indicated on
the device, and estimate one digit farther.
B. Significant Figures: The numbers that were
actually recorded in a measurement.
1. Rules for counting Significant Figures:
a. Nonzero’s are significant
b. Final zero’s after the decimal are significant
c. Zero’s that are between other significant figures are
significant.
How many significant figures are in each of the following numbers?
1)
2)
3)
4)
0.00240g
1.00240
1000L
1000.0L
Pg 146 Example 5.3 a-d
C. Exact Numbers: numbers determined by counting.
1. have unlimited significant digits.
Pg 146 Practice Problem Exercise 5.3 a-c
D. Significant Figures in Calculations: (How many digits
should I keep in my answer?)
1. Addition or subtraction:
The answer may hold as many decimal places as the
number from the problem that has the least decimal
places. (round to that place value)
12.11g + 18.0g + 1.013g = 31.123g
353.2mL + 17.89 mL= 371.09mL
183.062km – 14km = 169.062km
2. Multiplication or Division:
The answer may hold as many significant figures as the
number from the problem that has the least significant
figures. (round to that number of significant figures.
2
Pg4.56
149 m
Practice
Exercise
5.5 a-c
x 1.4mProblem
= 6.384m
8.315g
298L = 0.0279027g/L
Pg 150:/5-7
4.87m / 8.73g x 13m = 7.252 m2/g
5. How many sig. fig. should be in each result
a) 2
b) 1
c) 2
d) 3
6. Results
a) 5.4
b) 100
c) 5.0 x 107
d) 88500
7. Number of sig. figs in a measurement.
a) 2 (example is 14)
b) 3 (example is 3.14)
c) 2 (example is 4.6)
III. Problem Solving and Unit Conversions
You need two dozen doughnuts for advisory groups. Dunkin Donuts sells doughnuts for
A. Problem
$0.50 each.
How much willSolving:
the doughnuts cost?
1. Where do we want to go? What is the problem
asking for?
2. What do we know? List of facts.
3. How do we get there? What steps can we take to
solve the problem.
4. Does it make sense? Evaluate if the answer is
reasonable
Algebra Review
1.
2.
3.
4.
𝟏
=
𝟏
5
=
5
1.456
1.456
𝑥
=
𝑥
=
5. What’s the rule?
Anything divided by itself = 1
Algebra Review
1.
2.
3.
4.
5.
6.
5•1=
17 • 1 =
1.456 • 1 =
1,346,000.309534 • 1 =
x• 1 =
What’s the rule?
Anything multiplied by 1 stays the same.
Algebra Review
1.
2.
3.
4.
2𝑥
=
𝑥
4𝑥
=
2𝑥
6𝑥 2𝑦
• =
1
𝑥
3𝑦
45x • =
9𝑥
B. Converting Units of Measure: Changing the units of
a measurement but keeping the value the same.
1. Equivalence Statement: Shows two different #’s that are
thedoughnuts
same value.
(2.45cm
= 1 in.)
SeeDonuts
pg 153
You need two dozen
for advisory
groups.
Dunkin
sells doughnuts for
$0.50 each. 2.
HowConversion
much will theFactors:
doughnutsAcost?
(show
unit two
conversion)
ratio
thatusing
relates
units.
a.
They are made from the 2 parts of an equivalence statement.
»
b.
2.54𝑐𝑚
1𝑖𝑛.
or
1𝑖𝑛
2.54𝑐𝑚
A conversion factor allows us to cancel out a unit and replace it
with new unit.
Practice Problem 5.6 pg 156
Use Use
Table
Table
5.7 to
5.7make
to make
the following
the following
conversion.
conversion.
Convert
Convert
3.79kg
35.7qt
to
to L
2.37mi
tolbs.
m.
3. How to use a conversion factor to do a conversion
a.
b.
c.
d.
e.
Pg 170:2-4
Identify the equivalence statement(s) that will help with
this problem.
Write the number and unit given in the problem.
Multiply by a conversion factor (fraction) where
• The bottom has the unit you want to get rid of. (so it
cancels out)
• The top has the unit that you want to end up with.
Do the appropriate math.
Make sure you have the correct number of significant
figures. (look at the original measurement to determine sig.
figs.)
Conversion Factors and metric
Prefixes.
1 M__ = 106 __
1 k__
1
1
1
1
1
1
1
100
µ
Convert 35mg to g
Convert 7.38m to Mm
Convert 41.9kL to dL
=
1 d__ =
1 c__ =
1 m__ =
1 µ__ =
1 n__ =
103 __
10-1 __
10-2 __
10-3 __
10-6 __
10-9 __
C. Temp. Conversions
1. Celsius Scale: Based on the freezing and boiling point
of water
Tf = 0 oC
Tb = 100oC
2. Kelvin Scale: Base on absolute zero as the coldest
temp.
Tf = 273K
Tb = 373K
3. Conversions:
a. C K add 273 to the celcius temperature.
b. K  C subtract 273 from the kelvin temperature.
Complete the following conversions
-215
143oo Cto
Ctoto
K
oo C
198K
199K
C
D. Density: The amount of matter present in a
given volume of a substance.
1. Mass per unit of volume
2.
The density of a type of material is always the same. (ie. The
density of copper is 8.92g/mL)
• D=
1.
𝑔
( )
𝑚𝐿
𝑚
𝑣
m = mass (g)
D = Density,
V = volume (mL or cm3 )
Use this equation to determine the density, mass, or volume of
an object.
Density Problems
The
density
ofa apiece
rock
is
0.9980g/mL.
metalof
is 45.3g
1.113g/mL.
IfThe
a density
block
ofofstone
hasof
a mass
and takes up a
What
Whatisisthe
volume
mass of
ofwhat
the
a piece
rock
ifdensity?
the
metal
volume
with aismass
345mL?
of 1.45kg?
volume
ofthe
100.4mL,
is itsof