Metric Conversions – Dimensional Analysis

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Honors Chemistry
Riverside STEM Academy
Mrs. Hampton
All of the material from Chapter 3 of our text book, Prentice Hall Chemistry, has been covered in our
8th grade science course. Please review this chapter and complete these assignments. I recommend that
this be done towards the end of the summer break so that the material is fresh in your mind. The
material will be reviewed on the first day of school and a short 100 point placement test will be given on
the second day. We will begin the year with chapter 4, Atomic Structure. A power point is included in
this email to help you with the chapter 3 material. A scientific calculator is required every day. Be sure
to know how to use scientific notation on your calculator.
I will hold a tutorial session for students who need help in my classroom, Room 1, on Monday,
August 18 the week prior to school from 8:30 until 11:30 am.
Scientific Notation: Must be mastered prior to entering class. This will be a requirement for the course
but will not be taught. Make sure you are very comfortable with using scientific notation on your
calculator. Cell phones are not allowed during class so it is important that you become use to working
with your scientific calculator.
24,500
= 2.45 x 103
0.00045 = 4.5 x 10-4
6
1,230,000 = 1.23 x 10
0.55 = 5.5 x 10-2
Significant Figures: All answers throughout the year must be rounded off to the number of decimals as
the least accurate number given in the problem. 2 points will be deleted from all quiz and test answers
throughout the year that are rounded off to the wrong number of significant figures.
Significant
Figure Rule: all numbers are significant except place holders.
Number
Significant Figures
Reasoning
4,500
2
these zeroes are place holders and are not significant
4.50
3
this zero is an actual number and so is significant
0.405
3
zeroes between numbers are actual numbers
405
3
zeroes between numbers are actual numbers
0.00045
2
these zeroes are place holders and are not significant
0.0450
3
this zero is an actual number and so is significant
4,000,000
1
these zeroes are place holders and are not significant
Round off the answer to the proper number of significant figures (same sig figs as the least accurate
number in the problem.
Example: (4.2 x 10-7)(2.66 x 105) = 0.11
(only 2 sig figs allowed)
(6.702 x 103)(2.2 x 10-4) = 1.5
(only 2 sig figs allowed)
5.0 x 5.00 = 25
(only 2 sig figs allowed)
5.00 x 5.00 = 25.0
(3 sig figs allowed)
Metric System: Dimensional Analysis
Kilo
Deka
3
2
10 10 101 100
deci centi
10-1 10-2
milli
micro
nano
-3
-4
-5
-6
-7
-8
10 10 10 10 10 10 10-9
Convert these using dimensional analysis:
4.5 m to cm
0.55 mg to Kg
angstrom
pico
-10
-1 1
10
10
10-12
42,300 nl to dl
4.5 m 100 cm = 450 cm 0.55 mg Kg . = 5.5 x 10-7 Kg
42,300 nl
6
M
10 mg
Please email me if you have any questions: mhampton@rusd.k12.ca.us
dl = 4.23 x 10-4 dl
108 nl
Metric Conversions – Dimensional Analysis
Prefix
KiloHectoDekaDeciCentiMilliMicroNanoKilo
Deka
3
2
10 10 101 100
10x
103
102
101
100 = 1
10-1
10-2
10-3
10-6
10-9
Multiplier
1000
100
10
Meter gram liter
.1
.01
.001
.000001
.000000001
deci centi
10-1 10-2
milli
micro
nano
-3
-4
-5
-6
-7
-8
10 10 10 10 10 10 10-9
angstrom
pico
-10
-1 1
10
10
10-12
Metric System Practice
1.
2.
3.
4.
5.
6.
7.
8.
9.
What does the prefix Kilo- mean?
What does the prefix milli- mean?
What does the prefix Deka- mean?
What does the prefix deci- mean?
How many cm3 are in a dm3.
How many cm3 are in a liter.
Give another name for dm3.
Give another name for ml.
What is the definition of a gram?
10. Use dimensional analysis to convert
Example: 3.45 cg kg = 3.45 x 10-5 kg
105
0.466 dL
100 mL = 46.6 ml
dL
a. 42.4 milligram to kilograms
b. 6.7 x 107 nanometer to centimeters
c. 489.89 meters to nanometers
d. 68.09 kilometers to meters
e. 4.4 x 106 micrograms to centigrams
f. 78.009 milligrams to grams
g. 90.007 centigrams to nanograms
Liter = 1,000 ml = 1,000 cm3
h. 8.11 decigrams to milligrams
i. 44 kilometers to centimeters
j. 4400 Dekameters to micrometers
k. 2.2 cm to Km
l. 0.0011 g to mg
m. 800,000 cg to Kg
n. 0.0144 g to ng
o. 0.068 L to ml
p. 28,000 pL to cL
q. 0.0028 L to cL
The International System
1. What does the prefix Kilo- mean? 1,000
2. What does the prefix milli- mean? 0.001
3. What does the prefix Deka- mean? 10
4. What does the prefix deci- mean? 0.1
5. How many cm3 are in a dm3.
1,000
6. How many cm3 are in a liter.
1,000
7. Give another name for dm3.
liter
8. Give another name for ml.
cm3
9. What is the definition of a gram?
The amount of water in 1 cm3
10. Use dimensional analysis to convert
a. 42.4 milligram to kilograms
kg
= 4.24 x 10-5 kg
106 mg
b. 6.7 x 107 nanometer to centimeters
42.4 mg
6.7 x 107 nm
cm = 6.7 cm
107 nm
c. 489.89 meters to nanometers
489.89 m
109 nm
m
= 4.8989 x 1011 nm
d. 68.09 kilometers to meters
104 m = 6.809 x 104 m
Km
e. 4.4 x 106 micrograms to centigrams
68.09 Km
4.4 x 106 µg
cg
4
10 µg
= 4.4 x 102 cg
f. 78.009 milligrams to grams
78.9 mg
g
= 0.0789 g
3
10 mg
g. 90.007 centigrams to nanograms
90.7 cg
107 ng
cg
= 9.07 x 108 ng
h. 8.11 decigrams to milligrams
8.11 dg
102 mg
dg
= 811 mg
i. 44 kilometers to centimeters
105 cm
Km
44 Km
= 4.4 x 106 cm
j. 4400 Dekameters to micrometers
107
Dm
4400 Dm
k. 2.2 cm to Km
2.2 cm
µm
= 4.4 x 1010 µm
Km
= 2.2 x 10-5 Km
105 cm
l. 0.0011 g to mg
103 mg
g
0.0011 g
= 1.1 mg
m. 800,000 cg to Kg
800,000 cg
Kg
= 8 Kg
105 cg
n. 0.0144 g to ng
109 ng
g
0.0144 g
= 1.44 x 107 ng
o. 0.068 L to ml
0.068 L
103 ml
L
= 1.4 cg
p. 28,000 pL to cL
28,000 pL
= 2.8 x 10-6 cL
cL
1010 pL
q. 0.0028 L to cL
0.0028 L
102 cL
L
= 0.28 cL
Scientific Notation
1. Convert the following numbers from long form to scientific notation:
a. 744,510
e. 0.99
i. 0.0066
b. 330
f. 0.0004423
j. 1
c. 9,810
g. 34.5
k. 100
d. 241,000
h. 237,000
l. 23,000,000
2. Convert the following numbers to standard notation:
a. 3.25 x 103
e. 3.45 x 10-5
i. 2.3 x 103
b. 4.5 x 108
f. 8.9 x 103
j. 5.77 x 10-1
-4
-3
c. 7.10 x 10
g. 3.001 x 10
k. 4.0 x 104
6
-1
d. 2.8 x 10
h. 4.3 x 10
l. 2.33 x 10-5
3. Calculate the following and round off to 3 digits.
a. (7.83 x 104)(3.0)
b. (5.75 x 105)(9.9 x 102)
c. (2.99 x 105)(6.88 x 102)
d. (3.1 x 102)(1.22 x 104)
e. 4.51 x 103
2.0 x 105
f. 2.0 x 103
4.81 x 10-4
g. 2.30 x 10-4
2.0 x 104
h. 3.31 x 104
1.500 x 10-5
i. 2.100 x 102
1.00 x 108
j. 4.7 x 10-4
9.0 x 10-7
k. (1.2 x 102)(2.3 x 103)
l. (1.1 x 10-5)(7.0 x 10-4)
Scientific Notation
1. convert the following numbers from long form to scientific notation:
a. 744,510
e. 0.99
i. 0.0066
7.4451 x 105
9.9 x 10-1
b. 330
f. 0.0004423
3.3 x 102
6.6 x 10-3
j. 1
4.423 x 10-4
c. 9,810
g. 34.5
9.81 x 103
1 x 100
k. 100
3.45 x 101
d. 241,000
h. 237,000
2.41 x 105
1 x 102
l. 23,000,000
2.37 x 205
2. Convert the following numbers to standard notation:
a. 3.25 x 103
e. 3.45 x 10-5
2.3 x 107
i. 2.3 x 103
3,250
0.0000345
2,300
b. 4.5 x 108
f. 8.9 x 103
j. 5.77 x 10-1
8,900
0.577
g. 3.001 x 10-3
k. 4.0 x 104
0.003001
40,000
h. 4.3 x 10-1
l. 2.33 x 10-5
0.43
0.0000233
450,000,000
c. 7.10 x 10-4
0.00071
d. 2.8 x 106
2800000
3. Calculate the following and round off to 3 digits.
a. (7.83 x 104)(3.0)
= 2.3 x 105
b. (5.75 x 105)(9.9 x 102)
= 5.7 x 108
c. (2.99 x 105)(6.88 x 102)
= 2.1 x 108
d. (3.1 x 102)(1.22 x 104)
= 3.0 x 106
e. 4.51 x 103
2.0 x 105
= 2.3 x 10-2
f. 2.0 x 103
4.81 x 10-4
= 4.2 x 106
g. 2.30 x 10-4
2.0 x 104
= 1.2 x 10-8
h. 3.31 x 104
1.500 x 10-5
= 2.2 x 109
i. 2.100 x 102
1.00 x 108
= 2.1 x 10-6
j. 4.7 x 10-4
9.0 x 10-7
= 5.2 x 102
k. (1.2 x 102)(2.3 x 103) = 2.8 x 105
l. (1.1 x 10-5)(7.0 x 10-4) = 7.7 x 10-9
Significant Figures 1. Find the number of significant digits in each of the following.
a.
b.
c.
d.
e.
f.
g.
h.
0.00325
0.050
0.3304
12.00
14.0
14000
0.02
0.00101
i. 1200
j. 43.09
k. 20002
l. 23,000.
m. 1,000,000
n. 1,000.
o. 0.001100
p. 10900.0
2. Calculate the answers and round off to the correct number of significant figures.
a. (2.0)(2.0) =
i (10)(1200) =
b. (2.0)(2) =
j. (4.0)(3.00) =
c. (2.00)(2.000) =
k.(3)(4.0) =
d. (5.00)(5.00) =
l.(20.00)(2.00) =
e. (5.00)(5.0) =
m. (3.0)(4.00) =
f. 5 =
n. 0.02 =
5
0.0011
g. 7.0 =
o. 0.001 =
7.0
3.010
h. 1000 =
p. 18 =
1000
6.000
3.
Calculate the answers and round off to the correct number of significant figures and
PLACE IN SCIENTIFIC NOTATION!!!!!!!
a. (1.10 x 10-5)(7.9 x102)
b.
3.200 x 108 =
1.2 x10-7
h.
c. (2.000 x 105)(2.09 x10-9)
d.
7.4 x 10-2
=
6.400 x106
e. (2.33 x 107)(7.4 x10-5)
f.
g. (1.00 x 103)(7.4 x10-10)
=
2.2 x 10-3
=
6.000 x 104
=
=
3.20 x 106 =
4.100 x10-3
i. (1 x 103)(7.06 x10-9)
j.
=
2.3 x 1022
3 x103
=
=
k. (1.44 x 105)(2.000 x10-10)
l.
9.29 x 1033
6 x 10-19
=
=
Significant Figures 1. Find the number of significant digits in each of the following.
a. 0.00325
3
i. 1200
2
b. 0.050
2
j. 43.09
4
c. 0.3304
4
k. 20002
5
d. 12.00
4
l. 23,000.
5
e. 14.0
3
m. 1,000,000
1
f. 14000
2
n. 1,000.
4
g. 0.02
1
o. 0.001100
4
h. 0.00101
3
p. 10900.0
6
2. Calculate the answers and round off to the correct number of
significant figures.
a. (2.0)(2.0) = 4.0
i. (10)(1200) = 10,000
b. (2.0)(2) =
4
j. (4.0)(3.00) = 12
c. (2.00)(2.000) = 4.00
k. (3)(4.0) = 10
d. (5.00)(5.00) = 25.0
l. (20.00)(2.00) = 40.0
e. (5.00)(5.0) =
25
m. (3.0)(4.00) = 12
f. 5
5
1
n. 0.02 = 20
0.001
g. 7.0
7.0
=
=
1.0
o. 0.001 = 0.0003
3.00
h.
1000 =
1000
1
p. 18 = 3.0
6.000
3. Calculate the answers and round off to the correct number of
significant figures and
PLACE IN SCIENTIFIC NOTATION!!!!!!!
a. (1.10 x 10-5)(7.9 x102)
b.
3.200 x 108 = 2.7 x 1015
1.2 x10-7
c. (2.000 x 105)(2.09 x10-9)
d.
7.4 x 10-2
6.400 x106
=
2.2 x 10-3
6.000 x 104
=
4.18 x 10-4
1.2 x 10-8
e. (2.33 x 107)(7.4 x10-5)
f.
8.7 x 10-3
=
= 1.7 x 103
= 3.7 x 10-8
g. (1.00 x 103)(7.4 x10-10)
= 7.4 x 10-7
h.
3.20 x 106 =
4.100 x10-3
7.80 x 108
i. (1 x 103)(7.06 x10-9)
j.
2.3 x 1022
3 x103
= 7 x 10-6
= 8 x 1018
k. (1.44 x 105)(2.000 x10-10)
l.
9.29 x 1033
6 x 10-19
=
= 2.88 x 10-5
2 x 1052
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