Chapter 1: Measurements
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Transcript of Chapter 1: Measurements
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Chapter 1: Measurements
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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
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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
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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)
Cubic meter (m3)
Quart (qt) 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
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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
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. 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 2.7–2.8gives a final length reported as
2.75 cm
or 2.76 cm
Measured Numbers
2 3 4
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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
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Scientific Notation
• A number in scientific notation contains a coefficient and a power of 10.
coefficient power of ten coefficient power of ten
1.5 x 102 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
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Accuracy and Precision
• Accuracy - close to the actual value
• Precision - repeatability
Example: 3 darts are precise, but not accurate!
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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)
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Counting Sig Figs1. All non-zero digits are significant2. 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)
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Examples
Significant figures?
a.) 8.00 x 102 m
b.) 0.00002 L
c.) 600. in
d.) 20.60 mL
e.) 54,000 cm
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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
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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)
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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
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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
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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)
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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
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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
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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
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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
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Example
During surgery, a patient receives 5.0 pints of plasma. How many milliliters of plasma were given? 1 quart = 2pints
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Examplestep 1: Given 5.0 pints
step 2: pints quarts milliliters
step 3: 1 quart = 2pints and
1 quart = 946mL and
step 4:
1quart
2 p int s
2 p int s
1quart
1quart
946mL
946mL
1quart
5.0 p int s 1quart
2 p int s
946mL
1quart[2365] 2400mL
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Density
• The relationship between mass and volume
• Density can be used as a conversion factor
• Specific gravity is unitless but roughly equal to density numerically
Volume
MassDensity
erDensityWat
erialDensityMatavitySpecificGr
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Temperature
• 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
32)(8.1 CF
8.1
)32(
FC
C K 273
K o C 273