Mathematics Reivew
Name:__________________________
Semester 1 Unit 1: Intro to Physics
Date: _____________ Period: _______
1. Scientific Notation:
In our physics class we may deal with very large and very small numbers. This causes problems because often we have to
write many zeros. Scientists have learned to express these numbers as powers of 10.
Scientific notation has the general form of M x 10n, where 1 ≤ M ≤ 10 and n represents the number of decimal placed to
be moved from the expanded notation (i.e. 540000000). A positive value of n indicates the number is greater than one
(usually a large number). A negative value of n indicates the number is between zero and one (usually a small number).
Example 1: Convert 1300000 to scientific notation.
Answer: We move the decimal point so that there is only one digit to its left, a total of 6 places. If there is no decimal in
the expanded notation start counting from the last zero and remove all trailing zeros. ONLY REMOVE TRAILING
ZEROS IF THERE IS NO DECIMAL POINT.
1300000 = 1.3 x 106 (exponent is positive because number > 1)
Example 2: Convert 0.000047 to scientific notation.
Answer: For this, we move the decimal point 5 places to the right.
0.000047 = 4.7 x 10-5 (exponent is negative because number < 1)
Convert the following to scientific notation.
1. 0.005
____________________
6. 0.25
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2. 5050
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7. 0.025
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3. 0.0008
____________________
8. 0.0025
____________________
4. 1000
____________________
9. 500
____________________
5. 1000000
____________________
10. 5000
____________________
Convert the following to expanded notation.
1. 1.5 x 103
____________________
5. 2.2 x 105
____________________
2. 1.5 x 10-3
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6. 3.35 x 10-1
____________________
3. 3.75 x 10-2
____________________
7. 1.2 x 10-4
____________________
4. 3.75 x 102
____________________
8. 1 x 104
____________________
Perform the following calculations using your calculator.
1. (1.5 x 103)(3.75 x 102) =
______________________
2. (1.2 x 10-4)( 3.35 x 10-1) =
______________________
-2
______________________
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3. (3.75 x 10 ) / (2.2 x 10 ) =
1
2. Rearranging Algebraic Expressions:
When you first learn about an equation, it is usually shown in the following way. A symbol you haven’t seen
before is on the left of the equation. Symbols you’ve studied are on the right side of the equation. The value of
the quantity that the unfamiliar symbol represents can be found by performing mathematical operations on the
familiar quantities. The equation for density is shown below as an example.
𝐷=
𝑚
𝑉
Where D = Density, m = mass, V = volume
If you wish to calculate density, just put the known values for mass and volume into the equation. What do you
do, however, if you know the density of a substance as well as its volume, and you need to find the mass of the
substance? You start with the same equation but rearrange it. That way the values that you know—density and
volume—are both on the right side of the equation, and the unknown variable—mass—is by itself on the left
side, as shown below.
Example 1: Rearrange the density equation to solve for mass:
1. Write the standard equation.
𝐷=
𝑚
𝑉
2. If the variable you are trying to solve for is in numerator on the right hand side, flip the equation to put
the it on the left. In this case, by flipping we get the mass on the left.
𝑚
=𝐷
𝑉
3. The equation will still be true if you multiply both sides of the equation by the same amount. In this
case, multiply both sides by volume (V). this will cancel out the volume on the left side, leave the mass
alone on the left.
𝑚
𝑥𝑉=𝐷𝑥𝑉
𝑉
4. The equation has now be rearranged to solve for mass, the variable you want to solve. Now plug in your
values for density and volume and solve. Your units for density and volume should cancel out to leave
units of mass. If they don’t then you know you did something wrong.
m = DV
Example 2: Rearrange the density equation to solve for volume:
1. Write the standard equation.
𝐷=
𝑚
𝑉
2
2. if the variable you are trying to solve for is in denominator, multiple both sides of the equation by
volume (V). The equation will still be the same, and volume will be on the left side where you want it.
𝑚
𝑉𝑥𝐷=
𝑥𝑉
𝑉
So: DV = m
3. Now we have the variable for volume in the numerator on the left side, but it is not along. Now divide
both sides by density (D) to get the volume (V) alone on the left.
𝐷𝑉 𝑚
=
𝐷
𝐷
4. The equation has now be rearranged to solve for volume, the variable you want to solve. Now plug in
your values for density and mass and solve. Your units for density and mass should cancel out to leave
units of mass. If they don’t then you know you did something wrong.
𝑉=
𝑚
𝐷
Practice by rearranging the following equations to solve for the listed variable.
1. Rearrange the equation for the area of a rectangle (A = L x W) to solve for the length, L.
𝑑
2. Rearrange the equation for velocity (𝑣 = 𝑡 ) to solve for time.
3. Rearrange the equation, fn  n

2L
, to solve for L.
4. Rearrange the equation, 𝑣 = 𝑣𝑖 + 𝑎𝑡, to solve for t.
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2
5. Rearrange the equation, d  di  vi t  at 2 , to solve for t. Assume di = 0 and vi = 0.
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3.
Metric Conversions:
In the physics classroom and the lab, the metric system of measurement is used so it is important to be able to
convert from one unit to another.
Factor Label Method, GTA Method
1. Write the given number and unit – The G in GTA. (NO NAKED NUMBERS!)
2. Set up the conversion factor truth – The T in GTA (the fraction used to convert from one unit to another)
a. Place the given unit as the denominator of the conversion factor.
b. Place the desired unit in the numerator – your answer units.
c. Place a “1” in front of the larger unit.
d. Determine the number of smaller units needed to make “1” of the larger unit.
3. Multiply the given quantity by the conversion factor (truth) and solve for the answer – The A in GTA.
Remember to cancel out units!
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4.
Dimensional Analysis:
Using this method, it is possible to solve many problems by using the relationship of one unit to another, the
“T” in GTA. For example, 12 inches = 1 foot. Since these two measurements represent the same value, the
fractions 12 in/1 ft and 1 ft/12 in are both equal to one. When you multiple another number by the number one,
you do not change its value. However, you may change its unit.
Solve the following problems by using the GTA method. Show all work and include units.
1. 3.0 hours = _____ seconds
2. 12350 seconds = _____ hours
3. 1.3 years = _____ hours (1 year = 365 days)
4. 3.2 moles = _____ molecules (1 mole = 6.02 x 1023 molecules)
More on back 
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5. 2.5 x 1024 molecules = _____ moles
6. 30 mph (miles per hour) = _____ m/s (meters per second)
7. 9.8 m/s2 = _____ ft/s2 (feet per second2)
8. 30 m/s = _____ mph
9. 1.0 miles = _____ km
10. 2.0 km = _____ miles
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