Metric System Scientific Notation

1. +
Metric System &
Scientific Notation
Chemistry
August 20
th
/21
st
, 2009

2. +
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

3. +
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
meter
gram
liter
deci
(1/10)
centi
(1/100)
milli
(1/1000)

4. +
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)

5. +
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?

6. +
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
meter
gram
liter
deci
(1/10)
centi
(1/100)
milli
(1/1000)

7. +
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

8. +
Metric System
For each “step” to right,
you are multiplying by 10
For example, let’s go from a base unit to centi
1 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
meter
gram
liter
deci
(1/10)
centi
(1/100)
milli
(1/1000)

9. +
Kilo
(1000)
Hecto
(100)
Deca
(10)
Base Units
meter
gram
liter
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 centimeters
or
1.00 meter = 10.0 decimeters = 100. centimeters

10. +
Kilo
(1000)
Hecto
(100)
Deca
(10)
Base Units
meter
gram
liter
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)

11. +
Kilo
(1000)
Hecto
(100)
Deca
(10)
Base Units
meter
gram
liter
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

12. +
Kilo
(1000)
Hecto
(100)
Deca
(10)
Base Units
meter
gram
liter
deci
(1/10)
centi
(1/100)
milli
(1/1000)
Metric System
Now let’s start from centimeters and convert to
kilometers
400000 centimeters = ? kilometers

13. +
Kilo
(1000)
Hecto
(100)
Deca
(10)
Base Units
meter
gram
liter
deci
(1/10)
centi
(1/100)
milli
(1/1000)
Kilo
(1000)
Hecto
(100)
Deca
(10)
Base Units
meter
gram
liter
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

14. +
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
meter
gram
liter
deci
(1/10)
centi
(1/100)
milli
(1/1000)

15. +
Scientific Notation
Scientific notation is a way of expressing really big numbers Scientific notation is a way of expressing really big numbers
or really small numbers.or really small numbers.
For very large and very small numbers, scientific notation is For very large and very small numbers, scientific notation is
more concise.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 10
xx

16. +
Writing Scientific Notation
Place the decimal point so that there is Place the decimal point so that there is oneone non-zero non-zero
digit to the left of the decimal point.digit to the left of the decimal point.
Count the number of decimal places the decimal point Count the number of decimal places the decimal point
has “moved” from the original number. This will be the has “moved” from the original number. This will be the
exponent on the 10.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 10
88

17. +
Try this:
Given: 0.000567Given: 0.000567
Start with:
Decimal needs to move:
Answer:

18. +
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 10.Move the decimal point to the left for negative exponent 10.
(Use zeros to fill in places.)(Use zeros to fill in places.)
Example:Example:
Given: 5.093 x 10Given: 5.093 x 10
66
Move: 6 places to the right (positive)Move: 6 places to the right (positive)
Answer: 5,093,000Answer: 5,093,000

19. +
Try This:
Given: 1.976 x 10Given: 1.976 x 10
-4-4
Move:Move:
Answer: Answer: