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Metric System & Scientific Notation
ChemistryAugust 20th/21st, 2009
+Metric System
The metric system is based on a base unit that corresponds to a certain kind of measurement
Length = meter Volume = liter Weight (Mass) = gram
Prefixes plus base units make up the metric system Example:
Centi + meter = Centimeter Kilo + liter = Kiloliter
+Metric System
The three prefixes that we will use the most are: Kilo= 1000 centi = 1/100 (one hundredth) milli= 1/1000 (one thousandth)
How do you remember all of them?
Kissing Hairy Dark space dogs causes mono
Kilo(1000)
Hecto(100)
Deca(10)
Base Units
metergramliter
deci(1/10)
centi(1/100)
milli(1/1000)
+Metric System
So if you needed to measure length you would choose meter as your base unit Length of a tree branch
1.5 meters Length of a room
5 meters
But what if you need to measure a longer distance, like from your house to school? Let’s say you live approximately 10 miles from school
10 miles = 16093 meters 16093 is a big number, but what if you could add a prefix
onto the base unit to make it easier to manage: 16093 meters = 16.093 kilometers (or 16.1 if rounded to 1
decimal place)
+Typical Metric Units
What metric unit would you use to measure the length of the room?
What metric unit would you use to measure the distance between the mall and school?
What metric unit would you use to measure your weight?
What metric unit would you use to measure the amount of liquid in a soda bottle?
What unit would you use to measure the amount of liquid in an eye dropper?
+Metric System
These prefixes are based on powers of 10. What does this mean? From each prefix every “step” is either:
10 times larger or
10 times smaller For example
Centimeters are 10 times larger than millimeters 1 centimeter = 10 millimeters
Kilo(1000)
Hecto(100)
Deca(10)
Base Units
metergramliter
deci(1/10)
centi(1/100)
milli(1/1000)
+Metric System
Centimeters are 10 times larger than millimeters so it takes more millimeters for the same length
1 centimeter = 10 millimeters
Example not to scale
1 mm
1 mm
1 mm
1 mm
1 mm
1 mm
1 mm
1 mm
1 mm
1 mm
1 cm
40
41
41
40
+Metric System
For each “step” to right, you are multiplying by 10
For example, let’s go from a base unit to centi1 liter = 10 deciliters = 100 centiliters
2 grams = 20 decigrams = 200 centigrams
( 1 x 10 = 10) = (10 x 10 = 100)
(2 x 10 = 20) = (20 x 10 = 200)
Kilo(1000)
Hecto(100)
Deca(10)
Base Units
metergramliter
deci(1/10)
centi(1/100)
milli(1/1000)
+
Kilo(1000)
Hecto(100)
Deca(10)
Base Units
metergramliter
deci(1/10)
centi(1/100)
milli(1/1000)
Metric System
An easy way to move within the metric system is by moving the decimal point one place for each “step” desired
Example: change meters to centimeters
1 meter = 10 decimeters = 100 centimetersor
1.00 meter = 10.0 decimeters = 100. centimeters
+
Kilo(1000)
Hecto(100)
Deca(10)
Base Units
metergramliter
deci(1/10)
centi(1/100)
milli(1/1000)
Metric System
Now let’s try our previous example from meters to kilometers:16093 meters = 1609.3 decameters = 160.93 hectometers = 16.093
kilometers
So for every “step” from the base unit to kilo, we moved the decimal 1 place to the left (the same direction as in the diagram below)
+
Kilo(1000)
Hecto(100)
Deca(10)
Base Units
metergramliter
deci(1/10)
centi(1/100)
milli(1/1000)
Metric System
If you move to the left in the diagram, move the decimal to the left
If you move to the right in the diagram, move the decimal to the right
+
Kilo(1000)
Hecto(100)
Deca(10)
Base Units
metergramliter
deci(1/10)
centi(1/100)
milli(1/1000)
Metric System
Now let’s start from centimeters and convert to kilometers
400000 centimeters = ? kilometers
+
Kilo(1000)
Hecto(100)
Deca(10)
Base Units
metergramliter
deci(1/10)
centi(1/100)
milli(1/1000)
Kilo(1000)
Hecto(100)
Deca(10)
Base Units
metergramliter
deci(1/10)
centi(1/100)
milli(1/1000)
Metric System Now let’s start from meters and convert to
centimeters
5 meters = ? centimeters
• Now let’s start from kilometers and convert to meters
.3 kilometers = ? meters
+Metric System
Summary Base units in the metric system are meter, liter,
gram Metric system is based on powers of 10 For conversions within the metric system, each
“step” is 1 decimal place to the right or left Using the diagram below, converting to the right,
moves the decimal to the right and vice versa
Kilo(1000)
Hecto(100)
Deca(10)
Base Units
metergramliter
deci(1/10)
centi(1/100)
milli(1/1000)
+Scientific Notation
Scientific notation is a way of expressing really big Scientific notation is a way of expressing really big numbers or really small numbers.numbers or really small numbers.
For very large and very small numbers, scientific For very large and very small numbers, scientific notation is more concise.notation is more concise.
Scientific Notation always has two parts: A number between 1 and 9.9999…A number between 1 and 9.9999… A power of 10A power of 10
N x 10N x 10xx
+Writing Scientific Notation
Place the decimal point so that there is Place the decimal point so that there is oneone non- non-zero digit to the left of the decimal point.zero digit to the left of the decimal point.
Count the number of decimal places the decimal Count the number of decimal places the decimal point has “moved” from the original number. This point has “moved” from the original number. This will be the exponent on the 10.will be the exponent on the 10.
If the original number was less than 1, then the If the original number was less than 1, then the exponent is negative. If the original number was exponent is negative. If the original number was greater than 1, then the exponent is positive.greater than 1, then the exponent is positive.
Example: Given: 289,800,000Given: 289,800,000 Start with: 2.898 Start with: 2.898 Decimal needs to move 8 places to the rightDecimal needs to move 8 places to the right Answer: Answer: 2.898 x 102.898 x 1088
+Try this:
Given: 0.000567Given: 0.000567
Start with:
Decimal needs to move:
Answer:
+Change Scientific Notation back to Standard Form
Simply move the decimal point to the right for positive Simply move the decimal point to the right for positive exponent 10. exponent 10.
Move the decimal point to the left for negative exponent Move the decimal point to the left for negative exponent 10.10.
(Use zeros to fill in places.)(Use zeros to fill in places.)
Example:Example:
Given: 5.093 x 10Given: 5.093 x 1066
Move: 6 places to the right (positive)Move: 6 places to the right (positive)
Answer: 5,093,000Answer: 5,093,000
+Try This:
Given: 1.976 x 10Given: 1.976 x 10-4-4
Move:Move:
Answer: Answer: