Transcript APES Math PPT

Math Skills for APES
Calculations Without
Calculators
The Metric Mountain
• the prefix tells the scale of measurement
Know some basic metric prefixes for
simple conversions
Giga
G
10
9
Mega M
10
6
= 1 000 000
Kilo
k
10
3
= 1 000
Base
(m, l, g)
10
0
=1
Centi c
10
-2
= .01
Milli
m
10
-3
= .001
Micro μ
10
-6
= .000 001
n 10
-9
= .000 000 01
Nano
= 1 000 000 000
Metric Conversions
-7
10 m
• 2.50 x
to Mm
• 450 g to kg
• 56 cm to mm
All answers must use scientific
notation!
Use exponents whenever
numbers are especially
large or small.
Scientific notation is a way to
express, numbers the form of
exponents as the product of a
number (between 1 and 10) and
raised to a power of 10.
980 000  9.8 x 105
-4
0.000123  1.23 x 10
In scientific
notation
remember to
have one
number to the
left of the
decimal and to
use correct
significant
figures.
Scientific Notation
• 67 million
• 748 ten-thousandths
• 3 thousand
Math With Exponents
7
10
-19
10 =
• 5.6 x
x 3.1 x
3
2
• 244 x10 / 1.22 x 10 =
9
• 12,000 x 30 x 10 =
Practice math manipulations with
exponents
• When adding or subtracting
numbers with exponents the
exponents of each number must be
the same before you can do the
operation.
Example:
-3
-4
(1.9 x 10 ) – (1.5 x 10 )
(19 x 10-4 ) - (1.5 x 10-4 ) = 17.5 x 10-4
When multiplying numbers with
base 10 exponents, multiply the
first factors, and then add the
exponents.
Example, (3.1 x 105) (4.5 x 105) =
10
11
13.95 x 10 or 1.4 x 10
When dividing numbers, the
exponents are subtracted,
numerator exponent minus
denominator exponent.
Example:
5
9 x 10 = 3 x 10
3
3 x 10
2
Use Dimensional Analysis or factor/label
method for calculations
Given Value x Conversion factor
=Answer
1
OR
given unit x new unit = new unit
1 given unit
Example:
25 ft x 1 yd x 1.094 m =~ 9.12 meters
3 ft
1 yd
Conversion Factors will ALWAYS
be given
•
•
•
•
•
•
1kWh = 3400 BTU
1 BTU = 1050 J
2.2 = 1 kg
1 mi2 = 640 acres
1 ha = 10,000 m2 = 2.47 acres
1 metric ton = 2,205 lbs = 1,000 kg
Show ALL of your work and steps of
calculations, even if they are too simple.
Be sure to know how to convert numbers to
percentages and percent change.
Example: If 200 households in a
town of 10000 have solar power,
what percent does this
represent?
200/10000 x 100%= ?
Example: If a city of population
10,000 experiences 100 births, 40
deaths, 10 immigrants, and 30
emigrants in the course of a year,
what is its net annual percentage
growth rate?
Percent Change
• An unknown article states
that NOx emissions have
increased from 25 Gt to
130Gt annually. What is
the percent change in NOx
emissions?
Show all of your units, too!
Numbers given without units are
often not counted even if
correct.
Answers should make sense! LOOK them
over before you finish
Example:
No one is
going to
spend 1
billion
dollars per
gallon of
water!
Keep it simple. They don’t expect you to
do calculus!
Try reducing the
fraction from the
previous problem
200/1000 to 2/10=
1/5
Then solve:
1/5 x 100%= 20%
Doubling Time
• Rule of 70:
t=
70/r%
• Example: A country with a
population of 800 million has a
growth rate of 4% in 1990. In what
year will the population double?
Be able to calculate half life
A sample of radioactive waste has a halflife of 10 years and an activity level of 2
Example:
curies.
After how many
years will the activity
level of this sample be
0.25 curie?
Know how to graph data
•
•
•
•
•
Title the graph
Study Time
Set up the independent variable
along the X axis
100
90
Set up the dependent variable
along the Y axis
Label each axis and give the
appropriate units
Make proportional increments
along each axis so the graph is
spread out over the entire graph
area
Grade Percentages on Tests
•
•
80
70
60
50
40
30
20
10
0
Plot points and sketch a curve if
needed. Use a straight edge to
connect points unless told to
extrapolate a line
Label EACH curve if more than
one is plotted.
1
2
3
4
Hours per Week
5
6
Know what is meant by “per capita” when
solving a problem or interpreting a graph
Be able to interpolate and
extrapolate data
Remember that the numbers will
likely be simple to manipulate.
• If you are
getting
answers like
1.365, then it is
likely wrong