Number followed by a Unit from a
measuring device
SI Units (Le Système international d'unités)
– based on the metric system
Time
Length
Mass
Temperature
Amount of a substance
second (s)
meter (m)
kilogram (kg)
Kelvin (K)
mole (mol)
Metric Prefixes
What is Scientific Notation?
•Scientific notation is a way of
expressing really big numbers or
really small numbers.
•It is most often used in
“scientific” calculations where the
analysis must be very precise.
•For very large and very small
numbers, scientific notation is
more concise.
Scientific notation consists of
two parts:
•A number between 1 and 10
•A power of 10
N
x 10
x
Conversion factors
 Fractions in which the numerator and
denominator are EQUAL quantities expressed
in different units



Dimensional Analysis (Factor-label method)
A way of solving problems using conversion
factors
By using dimensional analysis the UNITS
ensure that you have the conversion factor in the
proper arrangement
Significant Figures
 The numbers reported in a
measurement are limited by the
measuring tool
 Significant figures in a
measurement include all; the
known digits plus one estimated
digit
Which of the two clocks below has the
potential to be the most accurate? Why?
Comparing Rulers
Zero as a Measured Number
. l3. . . . I . . . . I4 . . . . I . . . . I5. .
What is the length of the line?
First digit
Second digit
Last (estimated) digit is
cm
5.?? cm
5.0? cm
5.00 cm
Reading a Meterstick
. l2. . . . I . . . . I3 . . . .I . . . . I4. .
First digit (known)
=2
cm
2.?? cm
Second digit (known) = 0.7
2.7? cm
Third digit (estimated) between
0.05- 0.07
Length reported
=
2.75 cm
or
2.74 cm
or
2.76 cm
Rules for Significant Figures
adapted from Russo's Reliable Rules for Significant Figures
1. All non-zero digits are significant
2. Zeroes between non-zero digits are significant
3. In measurements containing an expressed decimal,
zeros to the right of NON-ZERO digits are significant.
“Atlantic - Pacific Rule”
Count from the ocean towards the coast starting with the first
nonzero digit, and include all the digits that follow.
Significant Numbers in Calculations
A calculated answer cannot be more precise
than the measuring tool.
A calculated answer must match the least
precise measurement.
Significant figures are needed for final
answers from
1) adding or subtracting
2) multiplying or dividing
Adding and Subtracting
The answer has the same number of decimal
places as the measurement with the fewest
decimal places.
Practice:
a) 2.45 cm + 6.382 cm + 5.8 cm
14.6 cm
b) 18.92 mL - 10.42 mL
8.50 mL
c) 22.100 g -13 g + 2.93g
12 g
Multiplying and Dividing
Round (or add zeros) to the calculated
answer until you have the same number of
significant figures as the measurement with
the fewest significant figures.
Practice:
a) 4.20 m x 3.21 m x 0.16 m
2.2 m3
b) 100.35 g / 90.2 mL
1.11 g/mL
c) (3.28 x 10-5 km) / (4 x 102 s)
8 x 10-8 km/s
• Fahrenheit
• Celsius
• Kelvin
Anders Celsius
1701-1744
Lord Kelvin
(William Thomson)
1824-1907
Boiling point
of water
Celsius
Kelvin
100 ˚C
373 K
100˚C
Freezing point
of water
0 ˚C
100 K
273 K
Notice that 1 kelvin = 1 degree Celsius
Calculations Using
Temperature
• Generally require temp’s in Kelvin
• K = ˚C + 273
• Body temp = 37 ˚C + 273 = 310 K
• Liquid nitrogen = -196 ˚C + 273 = 77 K
Derived Units – a combination of 2 or
more base units




Area
Speed
Volume
Density
(length x length)
(length per time)
(length x length x length)
(mass per volume)
Density 
Mercury
mass (g)
volume (cm3)
Platinum
Aluminum
13.6 g/cm3
21.5 g/cm3
2.7 g/cm3
A solid displaces a matching volume of
water when the solid is placed in water.
33 mL
25 mL
What is the density (g/cm3) of 48 g of a metal
if the metal raises the level of water in a
graduated cylinder from 25 mL to 33 mL?
1) 0.2 g/ cm3
2) 6 g/cm3
3) 252 g/cm3
Volume (mL) of water displaced
= 33 mL - 25 mL =
8 mL
Volume of metal (cm3)
= 8 mL x 1 cm3 =
1 mL
Density of metal =
mass
=
48 g
volume
8 cm3
8 cm3
= 6 g/cm3
Can you hit the bull's-eye?
Three targets
with three
arrows each to
shoot.
How do
they
compare?
Both
accurate
and precise
Precise
but not
accurate
Neither
accurate
nor precise
Can you define accuracy and precision?
How can someone show the accurate the
measurement?
Calculation of percent error
Percent Error (%) =
(Value accepted - Value experimental)
Value accepted
x 100
Graphing Data
1. Bar graphs
2. Circle graphs
3. Line graphs
Directly proportional
Inverse proportional