Chapter 1: Measurements
Chapter 1 Goals
• Learn the units and abbreviations for the metric
(SI) system
• Measured or exact number?
• Numbers in scientific notation
• Accuracy and precision
• Significant figures
• The use of prefixes to change base units
• Conversion factors
• Calculating temperature in Celsius, Fahrenheit,
and Kelvin
Metric (SI) System
• Decimal system based on 10
• Used in most of the world (NOT U.S.!)
• Used by hospitals and scientists
Know:
• Metric (SI) units for length, volume, mass
and temperature
Units of Measurement
Property
Metric Unit
US Unit
Conversion
Length
Meter (m)
Inch (in)
1m = 39.4 in
1in = 2.54 cm
Volume
Liter (L)
Quart (qt)
Cubic meter (m3)
1L = 1.06 qt
1qt = 946 mL
Mass
Gram (g)
Kilogram (kg)
Pound (lb)
1kg = 2.20 lb
1lb = 454 g
Temp
Celsius (ºC)
Kelvin (K)
Fahrenheit (ºF) 0 ºC, 32ºF, and
273K
* Metric (SI) units in bold
Measured and Exact Numbers
Measured Numbers:
• Device
• Uncertainty and error
in measurement
• An apple is measured
to be roughly 486g on
a top loading balance
Exact Numbers:
• From definition or
counting items
• The number of apples
in a sack is exactly 6
• There are exactly 12
inches in a foot
Measured Numbers
2
3
4
. l. . . . l . . . . l . . . . l . . . . l . .
cm
• To measure the length of the red line, we read
the markings on the meter stick.
The first digit
2
plus the second digit
2.7
• Estimating the third digit between 2.7–2.8
gives a final length reported as
2.75 cm
or
2.76 cm
Scientific Notation
•
•
•
•
Large Numbers: 12,000,000 = 1.2 x 107
Small Numbers: 0.00000012 = 1.2 x 10-7
Short hand: Mass of a proton = 1.67 x 10-27 kg
Easier to determine magnitude:
0.00000000000000000000000000167 kg
Scientific Notation
• A number in scientific notation contains a
coefficient and a power of 10.
coefficient power of ten
1.5
x
102
coefficient power of ten
7.35 x 10-4
• Place the decimal point after the first digit.
Indicate the spaces moved as a power of ten.
52 000 = 5.2 x 104
0.00378 = 3.78 x 10-3
4 spaces left
3 spaces right
Accuracy and Precision
• Accuracy - close to the
actual value
• Precision - repeatability
Example: 3 darts are precise, but not accurate!
Significant Figures
• Significant figures - all the reported numbers
including the estimated digit in measured
numbers only (not exact)
• All measured values have error
• Significant figures are used to track digits of
importance through calculations
• Good explanation of sig figs is given on page 10
(table 1.3)
Counting Sig Figs
1. All non-zero digits are significant
2. Zeroes may or may not be significant
Significant:
• Sandwiched between two non-zero digits
(607 m or 3.062 in)
• At the end of a decimal (80. L or 65.0 ºC)
• Any digit in the coefficient of a number in sci. not.
(5.50 x 103 m or 4.00 x 10-2 g)
Not significant:
• At the beginning of a decimal number (small number)
(0.0005 m or 0.015 g)
• Used as a place holder for a large number without a decimal
(530,000 m2 or 1,250,000 g)
Examples
Significant figures?
a.) 8.00 x 102 m
b.) 0.00002 L
c.) 600. in
d.) 20.60 mL
e.) 54,000 cm
Examples
Significant figures?
a.) 8.00 x 102 m - 3 sig figs
b.) 0.00002 L - 1 sig fig
c.) 600. In - 3 sig figs
d.) 20.60 mL - 4 sig figs
e.) 54,000 cm - 2 sig figs
Examples
Scientific notation?
a.) 60,800,000 sec (4sig figs)
b.) 0.00820 ft (2 sig figs)
c.) 0.00000345 L (3 sig figs)
d.) 2600 mL (3 sig figs)
Examples
Scientific notation?
a.) 60,800,000 sec (4 sig figs) - 6.080 x 107 sec
b.) 0.00820 ft (2 sig figs) - 8.2 x 10-3 ft
c.) 0.00000345 L (3 sig figs) - 3.45 x 10-6 L
d.) 2600 mL (3 sig figs) - 2.60 x 103 mL
Sig Figs in Calculations
• Rounding off:
– If first digit dropped is 4 or less the number is rounded down.
If it is 5 or more the number is rounded up
8.4234  8.42 (3 sig figs) or 8.4 (2 sig figs)
14.780  14.8 (3 sig figs) or 15 (2 sig figs)
• Multiplication and Division:
– The number with the lesser amount of sig figs determines the
sig figs in the answer
34.6 x 0.54 = 0.27804  0.28 (rounded to 2 sig figs)
67.2
Sig Figs in Calculations
• Addition and Subtraction:
– The number with the lesser amount of decimal places is
used to determine decimal places in the answer
5.048 + 45.1 = 50.148  50.1 (1 decimal place)
Metric and SI System Prefixes
Prefix
Abbreviation Conversion
Mega
M
1,000,000
Kilo
k
1,000
--
--
1
Centi
c
1/100
Milli
m
1/1,000
Micro
µ
1/1,000,000
Metric and SI System Prefixes
1000g = 1 kilogram (kg)
or
1g = 0.001kg
1m = 100centimeter (cm)
or
0.01m = 1cm
1L = 1000milliliters (mL)
or
0.001L = 1mL
Volume and Converting Cubic Units
•
•
•
•
•
1000 mL = 1 L
1 mL = 1 cm3 = 1 cc
100 cm = 1 m
100 cm3 IS NOT = 1 m3
(1m)3 = (100 cm)3 = 1,000,000 cm3
Conversion Factors
• Used for converting units and used A LOT in chemistry!
•
•
•
•
•
•
Step 1 – Identify information given
Step 2 – Plan how to reach desired units
Step 3 – Select necessary conversion factors
Step 4 – Set up conversions so they cancel
Step 5 – Solve problem and determine sig figs*
Unit should cancel leaving you with desired units
Example
During surgery, a patient receives 5.0 pints
of plasma. How many milliliters of plasma
were given? 1 quart = 2pints
Example
step 1: Given  5.0 pints
step 2: pints  quarts  milliliters
step 3: 1 quart = 2pints
and
1quart
2 p int s
1 quart = 946mL
1quart
946mL
and
2 p int s
1quart
946mL
1quart
step 4:
1quart 946mL
5.0 p int s 

 [2365]  2400mL
2 p int s 1quart
Density
Mass
Density 
Volume
• The relationship between
mass and volume
• Density can be used as a
conversion factor
• Specific gravity is
unitless but roughly equal
to density numerically
DensityMat erial
SpecificGravity 
DensityWat er
Temperature
 F  1.8(C )  32
( F  32)
C 
1.8
K  C  273
o
C  K  273
• Measures how hot or cold
things are
• Measure in Fahrenheit,
Celcius and Kelvin scales
• Can NOT be converted
simply using conversion
factors
• Different freezing temps
for each scale