Ch 2: A Mathematical Toolkit
I.
The SI Units (Systeme Internationale d’Unites)
Base Quantity
Length
Mass
Temperature
Time
Amount of Substance
Electric Current
Luminous Intensity
II.
Prefix
Femto
Pico
Nano
Micro
Milli
Centi
Deci
Kilo
Mega
Giga
Tera
III.
Base Unit
Meter
Kilogram
Kelvin
Second
Mole
Ampere
Candela
Symbol
m
Kg
K
s
mol
A
cd
SI Prefixes
Symbol
f
p
n
µ
m
c
d
k
M
G
T
Multiplier
1/1 000 000 000 000 000
1/1 000 000 000 000
1/1 000 000 000
1/1 000 000
1/1000
1/100
1/10
1000
1 000 000
1 000 000 000
1 000 000 000 000
Scientific Notation
10-15
10-12
10-9
10-6
10-3
10-2
10-1
103
106
109
1012
Example
femtosecond (fs)
picometer (pm)
nanometer (nm)
microgram (µg)
milligram (mg)
centimeter (cm)
deciliter (dL)
kilometer (km)
megagram (Mg)
gigameter (Gm)
terameter (Tm)
Scientific Notation
a. Shorthand: Move the decimal point until only one non-zero digit
remains on the left. Then count the number of places you moved the
decimal point and use that number as an exponent of 10. If you moved
the decimal point to the right, the exponent of 10 will be negative. If
you moved the decimal point to the left, the exponent of 10 will be
positive.
i. EX: average distance from the sun to Mars is 227 800 000 000m.
In scientific notation that would be 2.278 x 1011m.
ii. EX: mass of an electron is 0.000 000 000 000 000 000 000 000
000 000 911 kg. In scientific notation that would be 9.11 x 10-31
kg.
IV.
Converting Units: Factor-label Method
a. An easy way to convert a quantity expressed in one unit to that
quantity in another unit is to use a Conversion Factor, a relationship
between two units. A conversion factor is a multiplier equal to 1.
i. EX: Because 1 kg equals 1000g, you can construct the following
conversion factors:
1 = 1kg / 1000g or 1 = 1000g/1kg
ii. EX: Unit labels cancel just like algebraic quantities. This method
of converting one unit to another is called the Factor-Label
Method.
465g = (465g)(1kg / 1000g) = 465g x 1kg / 1000g = 0.465kg
V.
Significant Digits
a. The valid digits in a measurement are called the Significant Digits. Rules
for identifying Significant Digits:
i. All non-zero digits are significant.
ii. Zeros between two other significant digits are always significant.
iii. All final zeros after the decimal point are significant.
iv. Zeros used solely as placeholders are not significant
b. HINT: Written in scientific notation, the significant digits of any number
are equal to the number of digits multiplied by the power of 10.
Practice Problems
1)
Express the following quantities in scientific notation:
a. 450 000 m
b. 86 000 000 000 s
c. 0.000 508 kg
d. 0.0003600 kg
2)
Convert each of the following length measurements as directed:
a. 1.1 cm to meters
b. 76.2 pm to millimeters
c. 2.1 km to meters
d. 2.278 x 104 m to kilometers
3)
State the number of significant digits in each measurement:
a. 2804 m
b. 0.0029 m
c. 4.6 x 105 m
d. 75.00 m
e. 1.20 x 10-4 m