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Transcript of The SI System of Measurement. The Nature of Measurement Part 1 - number Part 2 - scale (unit)...
The SI System of Measurement
The Nature of Measurement
Part 1 - numberPart 2 - scale (unit)
Examples:20 grams
6.63 x 10-34 Joule·seconds
A Measurement is a quantitative observation consisting of TWO parts
The Fundamental SI Units (le Système International, SI)
Physical Quantity Name Abbreviation
Mass kilogram kg
Length meter m
Time second s
Temperature Kelvin K
Electric Current Ampere A
Amount of Substance mole mol
Luminous I ntensity candela cd
SI Base UnitsA base unit is a defined unit in a system of measurement that is based on an object or event in the physical world, and is independent of other units. Examples:1 Kg = The Legrand K
1 sec. = radiation frequency of a cesium-133 atom1 meter = distance light travels in 1/299,792,458th of a second.
SI Base Units
The SI base unit for temperature is the kelvin.• Most often confused with Celsius.
At zero kelvin, there exist virtually no particle motion or kinetic energy. This temperature is known as absolute zero.
SI Base Units
A unit that is defined by a combination of base units is called a derived unit.• Volume is a derived unit. Volume is
calculated by multiplying (length x width x volume).Volume is measured in cubic meters (m3), but this is very large. A more convenient measure is the liter, or one cubic decimeter (dm3).
• Density is a derived unit, g/cm3, the amount of mass per unit volume. Density is calculated by dividing (mass/volume)
SI PrefixesCommon to Chemistry
Prefix Unit Abbr. ExponentKilo k 103
Deci d 10-1
Centi c 10-2
Milli m 10-3
Micro 10-6
Metric ConversionsgmL 10-1 10-2 10-3101102103
Baseunit
deci centi millidekahectokilo
Conversions in the metric system are merely a matter of moving a decimal point. The “base unit” means the you have a quantity (grams, meters, Liters, etc without a prefix.
Metric ConversionsgmL 10-1 10-2 10-3101102103
Baseunit
deci centi millidekahectokilo
Example #1: Convert 18 liters to milliliters
18 L1 2 3
18 liters = 18 000 milliliters
Metric ConversionsgmL 10-1 10-2 10-3101102103
Baseunit
deci centi millidekahectokilo
Example #2: Convert 450 milligrams to grams
123450 mg450 mg = 0.450 g
Metric ConversionsgmL 10-1 10-2 10-3101102103
Baseunit
deci centi millidekahectokilo
Example #3: Convert 20 kilograms to milligrams
20 kg1 2 3 4 5 6
20 kg = 20 000 000 mg
Uncertainty and Significant Figures
Cartoon courtesy of Lab-initio.com
Uncertainty in Measurement
A digit that must be estimated is called uncertain. A measurement always has some degree of uncertainty.
Why Is there Uncertainty? Measurements are performed with instruments
No instrument can read to an infinite number of decimal places
Which of these balances has the greatest uncertainty in measurement?
Precision and AccuracyAccuracy refers to the agreement of a particular value with the true value.
Precision refers to the degree of agreement among several measurements made in the same manner.
Neither accurate nor
precise
Precise but not accurate
Precise AND accurate
Rules for Counting Significant Figures - DetailsNonzero integers always count as significant figures.
3456 has 4 significant figures
Rules for Counting Significant Figures - Details
Zeros- Leading zeros do not count as
significant figures.
0.0486 has3 significant figures
Rules for Counting Significant Figures - Details
Zeros- Captive zeros
always count assignificant figures.
16.07 has4 significant figures
Rules for Counting Significant Figures - Details
ZerosTrailing zeros are significant only if the number contains a decimal point.
9.300 has4 significant figures
Rules for Counting Significant Figures - Details
Exact numbers have an infinite number of significant figures.
1 inch = 2.54 cm, exactly
Sig Fig Practice #1How many significant figures in each of the following?
1.0070 m 5 sig figs
17.10 kg 4 sig figs
100,890 L 5 sig figs
3.29 x 103 s 3 sig figs
0.0054 cm 2 sig figs
3,200,000 2 sig figs
Rules for Significant Figures in Mathematical Operations
Multiplication and Division: # sig figs in the result equals the number in the least precise measurement used in the calculation.
6.38 x 2.0 =12.76 13 (2 sig figs)
Sig Fig Practice #2
3.24 m x 7.0 m
Calculation Calculator says: Answer
22.68 m2 23 m2
100.0 g ÷ 23.7 cm3 4.219409283 g/cm3 4.22 g/cm3
0.02 cm x 2.371 cm 0.04742 cm2 0.05 cm2
710 m ÷ 3.0 s 236.6666667 m/s 240 m/s
1818.2 lb x 3.23 ft 5872.786 lb·ft 5870 lb·ft
1.030 g ÷ 2.87 mL 2.9561 g/mL 2.96 g/mL
Rules for Significant Figures in Mathematical Operations
Addition and Subtraction: The number of decimal places in the result equals the number of decimal places in the least precise measurement.
6.8 + 11.934 =18.734 18.7 (3 sig figs)
Sig Fig Practice #3
3.24 m + 7.0 m
Calculation Calculator says: Answer
10.24 m 10.2 m
100.0 g - 23.73 g 76.27 g 76.3 g
0.02 cm + 2.371 cm 2.391 cm 2.39 cm
713.1 L - 3.872 L 709.228 L 709.2 L
1818.2 lb + 3.37 lb 1821.57 lb 1821.6 lb
2.030 mL - 1.870 mL 0.16 mL 0.160 mL
Scientific Notation
In science, we deal with some very LARGE numbers:
1 mole = 602000000000000000000000
In science, we deal with some very SMALL numbers:
Mass of an electron =0.000000000000000000000000000000091 kg
Scientific Notation
Imagine the difficulty of calculating the mass of 1 mole of electrons!
0.000000000000000000000000000000091 kg x 602000000000000000000000
???????????????????????????????????
Scientific Notation:A method of representing very large
or very small numbers in the form:
M x 10n
M is a number between 1 and 10
n is an integer
2 500 000 000
Step #1: Insert an understood decimal point
.
Step #2: Decide where the decimal must end up so that one number is to its leftStep #3: Count how many places you bounce the decimal point
123456789
Step #4: Re-write in the form M x 10n
2.5 x 109
The exponent is the number of places we moved the decimal.
0.0000579
Step #2: Decide where the decimal must end up so that one number is to its leftStep #3: Count how many places you bounce the decimal pointStep #4: Re-write in the form M x 10n
1 2 3 4 5
5.79 x 10-5
The exponent is negative because the number we started with was less than 1.
PERFORMING CALCULATIONS IN SCIENTIFIC
NOTATION
ADDITION AND SUBTRACTION
Review:Scientific notation expresses a number in the form: M x 10n
1 M 10n is an integer
4 x 106
+ 3 x 106
IF the exponents are the same, we simply add or subtract the numbers in front and bring the exponent down unchanged.
7 x 106
4 x 106
- 3 x 106
The same holds true for subtraction in scientific notation.
1 x 106
4 x 106
+ 3 x 105
If the exponents are NOT the same, we must move a decimal to make them the same.
4.00 x 106
+ 3.00 x 105 + .30 x 106
4.30 x 106Move the decimal on the smaller number!
4.00 x 106
A Problem for you… 2.37 x 10-6
+ 3.48 x 10-4
2.37 x 10-6
+ 3.48 x 10-4
Solution…002.37 x 10-
6
+ 3.48 x 10-4
Solution…0.0237 x 10-4
3.5037 x 10-4
Metric Conversion
Practice
Problem #1Convert 400 mL to Liters
400 mL= L
mL
L
1 000
1 .400
= 0.4 L
= 4x10-1 L
Problem #2Convert 10 meters to mm
10 m= m
mm
mm
1
1 000 10 000
= 1x104 mm
Problem #3Convert 73 grams to kg
73 g= kg
g
kg
1 000
1 0.073
= 7.3x10-2 kg
Problem #4Convert 0.02 kilometers to m
0.02 km= m
km
m
1
1 000 20
= 2x101 m
Problem #5Convert 20 centimeters to m
20 cm= m
cm
m
100
1 0.20
= 2x10-1 m
Problem #6Convert 450 milliliters to dL
450 mL= dL
mL
dL
100
1 4.5
Problem #7Convert 10 kilograms to grams
10 kg= g
kg
g
1
1 000 10 000
= 1x104 g
Problem #8Convert 935 mg to cg
935 mg= cg
mg
cg
10
193.5
= 9.35x101 cg
Problem #9Convert 5.2 kg to mg
5.2 kg= m
gkg
mg1
1 000 000
= 5 200 000 mg= 5.2x106 mg
Problem #10Convert 175 mL to cm3
175 mL= cm3
mL
cm3
1
1175
= 1.75x102 cm3
Representing Data: Graphs
A graph is a visual display of data that makes trends easier to see than in a table.
Parts of A Graph
Title
X- Axis : Independent VariableY- Axis: Dependent Variable
Description of variables
Types of Graphs
There are 3 main types of graphs that are used in science.1. Bar Graph2. Pie Chart/ Circle Graph3. Line Graph
Bar Graph
A bar graph is a visual display used to compare the amounts or frequency of occurrence of different characteristics of data. • This type of display allows us to: compare
groups of data, and. to make generalizations about the data quickly.
Pie Chart/ Circle Graph
A circle graph, or pie chart, has wedges that visually represent percentages of a fixed whole.
Line Graph
A line graph is useful for displaying data or information that changes continuously over time. Another name for a line graph is a line chart. • This is typically the most popular in
science.
Graph Interpretation
1. What is this graph about?2. At what age to teens have
the most cell phones?3. At what age do teens have
the least amount of cell phones?
4. How many cell phones do 15 yr. olds have?
5. How many cell phones do 16.5 yr. olds have?
6. What is the greatest number of cell phones at any age?
7. What is the lowest number of cell phones at any age?
Graph Interpretation
1. How many sectors does this graph have?
2. What percentage of people preferred chocolate Ice Cream?
3. If 50 people were surveyed how many people preferred Vanilla?