Exponents
Multiply or divide as indicated and express in proper scientific notation:
1.
2.
ሺ5.74 x 10଺ ሻሺ4.18 x 10ିସ ሻ =
ଽ.ଵଶ ୶ ଵ଴షల
ଷ.଼ ୶ ଵ଴ఴ
=
3.
7.62x10଺ doubled =
4.
7.62x10଺ squared =
Unit conversions
Relevant URLs with additional information and exercises for this topic include:
http://www.chem.tamu.edu/class/fyp/mathrev/mr-da.html
http://chemistry.alanearhart.org/Old/Tutorials/DimAnal/index.html
http://www.felderbooks.com/papers/units.html
Refresher: SI notation.
The metric system is correctly known as the SI system, which is short for Systeme International d'Unites
(International System of Units). The names of these base units are used in conjunction with standard
prefixes to refer to different quantities of a particular unit. All metric or SI prefixes refer to powers of 10.
The table below lists most of the SI prefixes.
SI Prefixes
Multiplier
Multiplier
(numerical)
(exponential)
(scientific notation)
Prefix
Symbol
tera
T
1 trillion
1,000,000,000,000
1012
1×1012
giga
G
1 billion
1,000,000,000
109
1×109
mega
M
1 million
1,000,000
106
1×106
kilo
k
1 thousand
1,000
103
1×103
hecto
h
1 hundred
100
102
1×102
deka
da
1 ten
10
101
1×101
1 one
1
100
1×100
0.1
10-1
1×10-1
UNIT
Meaning
Multiplier
deci
d
1 tenth
centi
c
1 hundredth
0.01
10-2
1×10-2
milli
m
1 thousandth
0.001
10-3
1×10-3
micro*
µ
1 millionth
0.000001
10-6
1×10-6
nano
n
1 billionth
0.000000001
10-9
1×10-9
pico
p
1 trillionth
0.000000000001
10-12
1×10-12
Notes: *The prefix µ, micro, should not cause confusion. The symbol for micro, the Greek letter mu (µ), is commonly
used in many scientific fields. The µm, a measure of small distances, is often popularly called the micron.
Show all conversion work, including all appropriate units, in the problem solutions. Full credit answers
will include conversion work. When appropriate, use scientific notation for your answers. Scientific
notation is typically used for numbers greater than 999 and less than 0.001.
Convert each of the quantities listed into the requested units. Write your answers in the blanks but
make sure to show your work in the spaces provided.
1. 610 m3 = _____________ km3
2. 2.3 g/mm3 = _______________ kg/cm3
3. 144 g/cm3 = ________________ kg/cm3
4. 8.3 cm/y = ____________ mm/d
5. 62 m/s = ______________ mm/d
Trigonometry
1. Solve for x:
30°
y
2. Solve for y:
x
3 cm
A
B
3. In the figure on the left, ABCD is a square whose side is 3 cm
units. Find the length of diagonal AD to the nearest tenth.
C
D
A ladder leans against a building. The foot of the ladder is 6 feet from the
building. The ladder reaches a height of 14 feet on the building.
4. Find the length of the ladder to the nearest foot.
5. Find, to the nearest degree, the angle the ladder makes with the ground.
Algebra and systems of equations
1. Solve for x:
4x + 5 = -2x + 17
x=
2. Solve the following system of equations for both x and y:
10x – y = 50
5x – 5y = 25
x=
y=
3. Factor the following equation as far as you can:
z ଷ − z ଶ − 9z + 9