Transcript APES Unit 1: Basic Math Review

Basic Math
Pre-assessment Review &
Practice Problems
Honors Environmental Science
Ms. Sipe
Scientific Notation
Scientific notation expresses very large or very small
numbers as a multiple of 2 numbers; Based on powers of
10
Ex. 6 x 1023
The 1st number
1≤ X<9
The 2nd number
is 10 raised to a power
The exponent is the # of places the decimal point must be
shifted to give the regular or standard notation. + rt and - lf
Scientific Notation Examples
Express the following in scientific notation
0.2713 =
314159 =
6022 =
0.12011 =
Express the following in standard or expanded form
4.44 x 10-6 =
7.121 x 109 =
1.2 x 10-1 =
1.8 x 102 =
Scientific Notation Answers
Express the following in scientific notation
0.2713 =
314159 =
6022 =
0.12011 =
2.713 X 10-1
3.14159 X 105
6.022 X 103
1.2011 X 10-1
Express the following in standard or expanded form
4.44 x 10-6 =
7.121 x 109 =
1.2 x 10-1 =
1.8 x 102 =
0.00000444
7,121,000,000
0.12
180
Scientific Notation Calculations
To X exponential terms add the powers; to / exponential
terms subtract. To + or – exponential terms, the exponents
must be the same.
Solve the following:
a. (3.0 x 10-8)(6.0 x 102) =
b. (2.0 x 104) ÷ (1.0 x 1013)=
c. (2.0 x 102) + (3.0 x 103) =
d. (2.5 x 103)(2.0 x 10-7) =
e. (7.0 x 101) =
(3.5 x 10-3)
f. (5.5 x 103) - (5.0 x 102) =
Scientific Notation Calculations Answers
To x exponential terms add the powers; to / exponential terms
subtract. To + or – exponential terms, the exponents must be
the same. Then, put the answer in proper scientific notation.
Solve the following:
a. (3.0 x 10-8)(6.0 x 102) = 1.8 X 10-5
b. (2.0 x 104) ÷ (1.0 x 1013)= 2.0 X 10-9
c. (2.0 x 102) + (3.0 x 103) = 3.2 X 103
d. (2.5 x 103)(2.0 x 10-7) = 5.0 X 10-4
e. (7.0 x 101) = 2.0 X 104
(3.5 x 10-3)
f. (5.5 x 103) - (5.0 x 102) = 5.0 X 103
-
SI The international system of units
Base Unit – need only one measurement
Derived Unit – a combination of 2 or more base units
Quantity
Definitions
Typical Unit
SI Unit
Base unit (B)
or
Derived unit
(D)
Equipment
Mass
Measure of the amount of matter
g
g
B
Triple beam
balance
Volume
Measure of the
Space that matter takes up
mL
D
Graduated
cylinder
Density
ratio of the mass of an object to its
volume.
g/cm3 or g/ml
D
Length
distance
between two points
m
m
B
Ruler
Time
Duration of an event
s
s
B
Stop watch,
clock, timer
Temperature
Measure of KE (vibration of
molecules)
°C
K
B
thermometer
The Metric System and Prefixes
/
103
102
101
100
10-1
10-2
10-3
X
The Metric System and Prefixes
Also should
also know:
Tera (T) 1012
Giga (G) 109
Mega (M) 106
Micro (u) 10-6
Nano (n) 10-9
Pico (p) 10-12
METRIC CONVERSIONS USING DIMENSIONAL ANALYSIS:
1,000,000 µg = 1g
1,000,000 µL = 1 L
1,000mg = 1 g
1,000mL = 1 L
100cg = 1 g
100cL = 1 L
10dg = 1 g
10dL = 1 L
1 kg = 1,000g
1 kL = 1,000 L
Metric Conversions
1.
876 milliliters to liters
5) 11.7 grams to kilograms
2.
78,999 milligrams to grams
6) 0.0009 kiloliters to liters
3.
0.9 centigrams to grams
7) 44 centimeters to meters
4.
112 meters to millimeters
8) 277 kilograms to grams
Metric Conversion Answers
1.
876 milliliters to liters
876ml(1L/1000mL) = 0.876 L
5) 11.7 grams to kilograms
11.7g (1 kg/1000g) = 0.011700
2. 78,999 milligrams to grams
78,999mg(1g/1000mg) = 78.999 g
6) 0.0009 kiloliters to liters
0.0009kL(1000L/1kL) =0.9 L
3.
7) 44 centimeters to meters
44cm(1m/100cm) = 0.44 m
0.9 centigrams to grams
0.9cg(1g/100cg)0.009 g
4. 112 meters to millimeters
112m(1000mm/1m) = 112,000 mL
8) 277 kilograms to grams
277kg(1000g/1kg)= 277,000 g
Dimensional Analysis
•
•
•
•
What’s given?
What do you want?
Look for an equivalence statement to put into ratio form
Show all work
– Set-up (bridge) with all units
– May have one or multiple steps
• Did you answer the question? Is the answer reasonable?
Dimensional Analysis Practice
Given:
2.54 cm = 1 inch
3.79 L = 1 gallon
16 ounces = 1 pound
1 L = 1000 mL
1 mile = 5280 feet
454 g = 1 pound
1 calorie = 4.18 Joules
1 mole = 6.02 X 1023 atoms
1 gallon = 4 quarts
1 ft = 12 inches
1 mL = 1 cm3
Solve:
5.7 inches = _____________ cm
125 grams = ______________ lbs
2.5 miles = ______________ feet
85 ounces = ________________ lbs
72 cm3 = ______________ mL
4 moles = ________________ atoms
Dimensional Analysis Answers
Solve:
5.7 inches = _____________ cm
5.7in(2.54cm/1in) = 14.478cm
85 ounces = ________________ lbs
85oz(1lb/160z) = 5.31lbs
125 grams = ______________ lbs
125g(1lb/454g) = 0.28lbs
72 cm3 = ______________ mL
72 cm3(1mL/1cm3)= 72mL
2.5 miles = ______________ feet
2.5mi(5280ft/1mi)= 13200ft
4 moles = ________________ atoms
4mol(6.022X 1023 atoms/1mol)=
2.41 X 1024 atoms
More to Come:
Nuclear Chemistry reactions & calculations.
Concentration reactions & calculations