Math Practice
Example 1: Solving for a variable
This astronomy lab requires some basic math skills. You should be
able to solve equations for a certain variable.
In the equation
1/f = 1/u - 1/v,
you should be able to solve for f.
This exact formula will be used in Lab 3 and is called the lensmaker's
formula.
Example 2: Fun With Fractions
It is important to feel comfortable with fractions (note: example 1 deals
with fractions). Besides being able to solve for a variable, as in example 1,
understanding
the basic properties of fractions will be extremely helpful.
| Cross Multiplying: |
x/y = 3/2 can also be written as 2x = 3y |
| Fraction Multiplication: |
(9/5)*(10/3)=6 |
| Fraction Division: |
(9/5)/(10/3) = (9/5)*(3/10) = 27/50 = 0.54 |
If you don't know how I got these answers then you should review an
algebra book, ask a friend, or talk to me.
Example 3: Math Functions
You should be able to solve the following equations, using a
scientific calculator:
d=10^[((15.5-5.3)/5)+1].
If you are unfamiliar with this notation then you should review your
math text book, ask a friend, or ask me. It only takes a few minutes
to review this notation. Also, it is important to remember the order that
the math functions follow.
Begin with the innermost set of parenthesis and move outward.
- Division and Multiplication from left to right.
- Addition and Subtraction from left to right.
Example 4: Converting by using a scale
Many students have difficulty using a scale to convert the units of a
measurement. I think it is important to review the concept before trying
to use it so that the lab process won't feel intimidating or confusing.
The purpose of converting is to change the units of a measurement into
something that will be more useful to us.
Here are two simple examples:
-
We know that for every
foot there are 12 inches. This ratio is also known as a SCALE,
which can be written as 1foot=12inches or 1foot/12inches.
Knowing this scale, let's convert my height from feet to inches. I
am 5 feet 2 inches tall. What is my height in inches?
First, I need to convert 5 feet to inches:
(5feet)*(12inches/1foot) = 60 inches
But, my height is 5 feet 2 inches, not just 5 feet. So, I need to add in
the extra two inches.
60 inches + 2 inches = 62 inches
All I did was multiply my known quantity by my SCALE in order to
change my units.
-
The second example involves the roadmaps used when driving.
The map is obviously not life size. It has been SCALED down so
that the map can be used inside of a vehicle. Therefore, the map usually
provides a scale that tells you, for example, 3 inches is equal to 60 miles.
Again, this is your conversion SCALE and will be
used to convert inches to
miles (3 inches = 60 miles OR 3inches/60 miles OR 1inch/20miles). Therefore,
if you look at a road map, and you see that the distance between
Tuscaloosa and Meridian is approximately 4.5 inches then how far away,
in miles, is Meridian?
(Distance in inches)(SCALE)=(Distance in miles)
(4.5inches)(20miles/1inch) = (90 miles)
If you don't understand
how the unit converstion works here then you should review your math book,
ask a friend, or see me.