Physics Fix 1 & 2
Name: ______________________________
Date: _____________
Hour: _____
Information: Units
The following tables contain common metric (SI) units and their prefixes.
Table 1: metric base units
Quantity
Length
Mass
Time
Temperature
Volume
Amount of substance
Unit
meter
kilogram
second
Kelvin
Liter
mole
Table 2: prefixes for metric base units.
Prefix
Symbol
Mega
M
Kilo
k
Deci
d
Centi
c
Milli
m
Micro

Nano
n
Pico
p
Unit Symbol
m
kg
s
K
L
mol
Meaning in Words
million
thousand
tenth
hundredth
thousandth
millionth
billionth
trillionth
Meaning in Numbers
1,000,000
1,000
0.1
0.01
0.001
0.000001
0.000000001
0.000000000001
Note the following examples:
 “Mega” means million so “Megagram” (Mg) means one million grams NOT one
millionth of a gram. One millionth of a gram would be represented by the microgram
(g). It takes one million micrograms to equal one gram and it takes one million
grams to equal one Megagram.
 One cm is equal to 0.01 m because one cm is “one hundredth of a meter” and 0.01 m
is the expression for “one hundredth of a meter”
Critical Thinking Questions
1. “Milli” means “thousandth” so a milliliter (symbol: mL) is one thousandth of a Liter.
Therefore, it takes _____________ mL to make one L
2. “Kilo” means “thousand” so a kiloliter contains ____________ Liters?
how many?
3. How many milligrams are there in one kilogram?
4. How many meters are in 21.5 km?
5. Is it possible to answer this question: How many mg are in one km? Explain.
6. Which is larger one Mm or one mm?
Information: Scientific Notation
“Scientific notation” is used to make very large or very small numbers easier to handle. For
example the number 45,000,000,000,000,000 can be written as “4.5 x 1016 ”. The “16” tells you
that there are sixteen decimal places between the right side of the four and the end of the number.
Another example: 2.641 x 1012 = 2,641,000,000,000  the “12” tells you that there are
12 decimal places between the right side of the 2 and the end of the number.
Very small numbers are written with negative exponents. For example, 0.00000000000000378
can be written as 3.78 x 10-15. The “-15” tells you that there are 15 decimal places between the
right side of the 3 and the end of the number.
Another example: 7.45 x 10-8 = 0.0000000745  the “-8” tells you that there are 8
decimal places between the right side of the 7 and the end of the number.
In both very large and very small numbers, the exponent tells you how many decimal points are
between the right side of the first digit and the end of the number. If the exponent is positive, the
decimal places are to the right of the number. If the exponent is negative, the decimal places are
to the left of the number.
Critical Thinking Questions
7. Two of the following six numbers are written incorrectly. Circle the two that are incorrect.
a)
3.57 x 10-8
104
b)
4.23 x 10-2
c)
75.3 x 102
d)
2.92 x 109
What do you think is wrong about the two numbers you circled?
8. Write the following numbers in scientific notation:
e)
0.000354 x 104
f)
9.1 x
a) 25,310,000,000,000,000 = _____________
b) 0.000000003018 = ____________
9. Write the following scientific numbers in regular notation:
a) 8.41 x 10-7 = ________________
b) 3.215 x 108 = _____________________
Information: Multiplying and Dividing Using Scientific Notation
When you multiply two numbers in scientific notation, you must add their exponents. Here are
two examples. Make sure you understand each step:
(4.5x1012) x (3.2x1036) = (4.5)(3.2) x 1012+36 = 14.4x1048  1.44x1049
(5.9x109) x (6.3x10-5) = (5.9)(6.3) x 109+(-5) = 37.17x104  3.717x105
When you divide two numbers, you must subtract denominator’s exponent from the numerator’s
exponent. Here are two examples. Make sure you understand each step:
2.8 x1014 2.8

x10147  0.875 x107  8.75 x106
7
3.2 x10
3.2
5.7 x1019 5.7

x1019  ( 9 )  1.84 x1019  9  1.84 x10 28
9
3.1
3.1x10
Critical Thinking Questions
11. Solve the following problems.
a) (4.6x1034)(7.9x10-21) =
b) (1.24x1012)(3.31x1020) =
12. Solve the following problems.
a)
8.4 x10 5

4.1x1017
b)
5.4 x10 32

7.3 x1014
Information: Adding and Subtracting Using Scientific Notation
Whenever you add or subtract two numbers in scientific notation, you must make sure that they
have the same exponents. Your answer will them have the same exponent as the numbers you
add or subtract. Here are some examples. Make sure you understand each step:
4.2x106 + 3.1x105  make exponents the same, either a 5 or 6  42x105 + 3.1x105 = 45.1x105 =
4.51x106
7.3x10-7 - 2.0x10-8  make exponents the same, either -7 or -8  73x10-8 – 2.0x10-8 = 71x10-8 =
7.1x10-7
Critical Thinking Questions
13. Solve the following problems.
a) 4.25x1013 + 2.10x1014 =
b) 6.4x10-18 – 3x10-19 =
c) 3.1x10-34 + 2.2x10-33 =
CONVERTING UNITS
Information: Dimensional Analysis
“Dimensional Analysis” is a big scary term that doesn’t really need to be scary. It’s simple. The
basis for dimensional analysis is this: if you multiply something by 1 you do not change its
value! Pretty easy, eh? Here’s an example:
1 3 3
 
2 3 6
Notice that the value of ½ didn’t really change because 3/3 is the same as 1. Again, in
mathematics, multiplying by 1 doesn’t change the real value of anything.
100 cm
3
3
100 cm
is a fraction t hat behaves just like because 100cm  1 meter! Therefore, neither nor
1 meter
3
3
1 meter
will change the real value of a number.
Here’s an example problem of a conversion:
Convert 3.75 cm into meters. All you need to do is multiply by a fraction.
Always begin by
putting the number
you are given in a
fraction over 1.
Find a fraction that contains both
units that you are working with.
Here we have cm and m.
Notice that 1 m and 100 cm equal each other. THIS IS A
MUST. You could also have “0.01 m” and “1 cm”
because 0.01 m = 1 cm.
3.75 cm
1m
3.75 cm  1m 3.75 cm  1m



 0.0375 m
1
100 cm
1  100 cm
1  100 cm
We put cm on the bottom
here so that it cancels here.
m is the only
unit left and it’s
the unit we
want
Notice in the above example that cm was on the bottom in the conversion factor fraction. This is
very important. “Tops and bottoms cancel each other.” We need cm on the bottom so that it
cancels out the one on the top!
Critical Thinking Questions
1. If you were converting 42 grams into kilograms, which fraction would you use as a
converting factor?
A)
1000 g
1 kg
B)
1000 kg
1g
C)
1 kg
1000 g
D)
1g
1000 kg
Explain your reasoning:
2. How many meters are in 32.5 kilometers? (You are converting km to m.)
The problem is started for you:
32.5 km


1
3. How many L are there in 32.5 L?
Information: Non-base unit  non-base unit
So far we have been converting a prefixed unit into a base unit or vice versa. It gets a little more
complex when we want to convert a prefixed unit into another prefixed unit. Whenever such is
the case, convert to the base unit first and then finish the problem.
For example, if you needed to convert centimeters into kilometers, first convert to the base
unit—meters. Then convert meters into kilometers.
Critical Thinking Questions
4. How many cm are there in 40 km? Let’s break it into two steps…
a) First, convert to the base unit, which for this problem is meters. Fill in the blanks.
40 km

1
m
 ______________________
km
km is on the bottom to cancel out the
other km, which is on the top.
m and km are chosen because we are
converting from km to m
b) Now convert your answer to part a (which is in meters) into centimeters.
m
1
5. How many kL are there in 34,500 mL?

km

m
a) First, convert mL to L.
b) Now convert your answer to part a (in L) to kL.
6. How many m are there in 0.0035 km?
Information: Quantities containing two units at once
It gets a bit more complicated if we have to convert a quantity containing two units. For
example, speed has two units. “Miles per hour” contains two units. “Meters per second”
contains two units. When you need to do a conversion on such a quantity, do one unit at a time.
Here’s an example.
Convert 50 km/hr to m/s.
hr is on the top here so that it cancels
with the hr on the bottom. “Tops and
bottoms cancel.”
50 km 1000 m
1 hr
1 min 50 km  1000 m  1 hr  1 min




 13.89 m/s
1 hr
1 km
60 min 60 s
1 hr  1km  60 min  60 s
First we converted
km then we’ll work
on the hr.
Critical Thinking Questions
7. Convert 25 m/s to km/hr.
8. The speed of sound is approximately 340 m/s. How many km/hr is that?
9. The maximum highway speed in Michigan is 70 miles/hr. How many km/hr is this? (Note:
1 mile is equal to 1609 m.)
10. The flow of water in our kitchen tap is 3.2 L/min. How many mL/s is this?