 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

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
deci
(1/10)
centi
(1/100)
Base Units
Kilo
(1000)
Hecto
(100)
Deca
(10)
meter
gram
liter
milli
(1/1000)

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 approx. 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)





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?
 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
Base Units
Kilo
(1000)
Hecto
(100)
Deca
(10)
meter
gram
liter
deci
(1/10)
centi
(1/100)
milli
(1/1000)
• Centimeters are 10 times
larger than millimeters so it
takes more millimeters for
the same length
1 centimeter = 10 millimeters
(Example not to scale)
40
1 mm
40
1 cm
41
1 mm
1 mm
1 mm
1 mm
1 mm
1 mm
1 mm
1 mm
1 mm
41
 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
( 1 x 10 = 10) = (10 x 10 = 100)
2 grams = 20 decigrams = 200 centigrams
(2 x 10 = 20) = (20 x 10 = 200)
Base Units
Kilo
(1000)
Hecto
(100)
Deca
(10)
meter
gram
liter
deci
(1/10)
centi
(1/100)
milli
(1/1000)
 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
Base Units
Kilo
(1000)
Hecto
(100)
Deca
(10)
meter
gram
liter
deci
(1/10)
centi
(1/100)
milli
(1/1000)
 Now
let’s try our previous example from meters
to kilometers:
16093 meters = 1609.3 decameters = 160.93
hectometers = 16.093 kilometers
Base Units
Kilo
(1000)
 So
Hecto
(100)
Deca
(10)
meter
gram
liter
deci
(1/10)
centi
(1/100)
milli
(1/1000)
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)
 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
Base Units
Kilo
(1000)
Hecto
(100)
Deca
(10)
meter
gram
liter
deci
(1/10)
centi
(1/100)
milli
(1/1000)
 Now
let’s start from centimeters and convert to
kilometers
400000 centimeters = ? kilometers
Base Units
Kilo
(1000)
Hecto
(100)
Deca
(10)
meter
gram
liter
deci
(1/10)
centi
(1/100)
milli
(1/1000)
Now let’s start from meters and convert to centimeters
5 meters = ? centimeters
Base Units
Kilo
(1000)
Hecto
(100)
Deca
(10)
meter
gram
liter
deci
(1/10)
centi
(1/100)
milli
(1/1000)
Now let’s start from kilometers and convert to meters
0.3 kilometers = ? meters
Base Units
Kilo
(1000)
Hecto
(100)
Deca
(10)
meter
gram
liter
deci
(1/10)
centi
(1/100)
milli
(1/1000)
 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
Base Units
Kilo
(1000)
Hecto
(100)
Deca
(10)
meter
gram
liter
deci
(1/10)
centi
(1/100)
milli
(1/1000)
Accuracy vs. Precision
Accuracy: measurements are close to true (“correct”) value
Precision: measurements are consistent/ reproducible;
measurements are close to each other.
Significant Figures
What are they?
• A way to indicate the accuracy of a
measurement or calculations involving
measurements.
• Significant figures in a measurement
include all the digits known with certainty
plus one final digit, which is estimated.
Significant Figures
1
2
3
4
5
5
1
2
3
4
5
1
2
3
4
5
Rules for Significant Figures
Non-Zero Rule: All digits 1 – 9 are always • 2.35 g has three sig figs
• 2251 g has two sig figs
significant.
Righty-Righty Rule: Zeros at the end of a • 205 m has three sig figs
number and to the right of a decimal point
• 80.04 m has four sig figs
ARE significant.
Straddle Rule: Zeros appearing between
significant digits ARE significant.
Beginning Zeros Rule: Zeros appearing to
the left of ALL non-zero digits are NOT
significant.
Ending Zeros rule: Zeros at the end of a
number, but to the left of the decimal
place are NOT significant.
Decimal Point Rule: A decimal point may
be used to indicate the significance of
zeros to the left of it.
• 2.30 mL has three sig figs
• 20.0 mL has three sig figs
• 0.095 897 m has five sig figs
• 0.000 09 L has one sig fig
• 3500 kg has two sig figs
• 10,000 m has one sig fig
• 3500 g has two sig figs
• 3500. g has four sig figs
Significant Figures Examples
All figures are
significant
(4 sig figs)
All figures are
Significant
(5 sig figs)
Zeros between
Non-zeros ARE
significant
Zero to the
right of the
decimal ARE
significant
Significant Figures Examples
No decimal
point
2 sig
figs
Zeros are not
significant!
Decimal
Point
All digits including
zeros to the left of
The decimal are
significant.
6 sig figs
Significant Figures Examples
3 sig figs
Zeros to the right of the decimal
with no non-zero values before the
decimal are not significant
5 sig figs
Zeros to the right of the decimal
And to the right of non zero values
Are significant
How many significant figures are in
each of the following measurements?
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
28.6 g
3440. cm
910 m
0.046 04 L
0.006 700 0 kg
804.05 g
0.014 403 0 km
1002 m
400 mL
30,000. cm
0.000 625 000 kg
•
•
•
•
•
•
•
•
•
•
•
Three
Four
Two
Four
Five
Five
Six
Four
One
Five
Six
Significant Figures
Rules for Addition & Subtraction
When adding or subtracting decimals, the
answer must have the same number of digits
to the right of the decimal point as there are
in the measurement having the fewest digits
to the right of the decimal point.
25.1 g + 2.03 g = 27.13 g
= 27.1 g
Significant Figures
Rules for Addition & Subtraction
The numbers in
these positions are
not zeros, they are
unknown
The sum of an
unknown number
and a 6 is not valid.
The same is true
For the 2
The answer is rounded to the
position of least significance
Significant Figures
Rules for Multiplication & Division
For multiplication and division, the answer
can have no more significant figures than
are in the measurement with the fewest
number of significant figures.
1. What is the sum of 2.099 g and 0.05681 g?
 2.156 g
2. Calculate the quantity 87.3 cm – 1.655 cm.
 85.6 cm
3. What is the density of a substance with a
mass of 1.425 g and a volume of 2.1 mL?
 0.68 g/mL
4. Calculate the area of a crystal surface that
measures 1.34 mm by 0.7488 mm.
 1.00 mm2
5. 1.35 m x 2.467 m = __________
 3.33 m2
6. 1,035 m2  42 m = __________
 25 m
7. 12.01 mL + 35.2 mL + 6 mL = __________
 53 mL
8. 55.46 g – 28.9 g = __________
 26.6 g
9. 0.021 cm x 3.2 cm x 100.1 cm = __________
 3.7 cm3
10. 0.15 cm + 1.15 cm + 2.051 cm = __________
 3.35 cm
11. 150 L3  4 L = __________
 40 L2
12. 505 kg – 450.25 kg = __________
 55 kg
13. 1.252 cm x 0.115 cm x 0.012 cm = __________
 0.0017 cm3
14. 4.6 m – 2.15 m + .08 m = __________
 2.5 m
Significant Figures
& Exact Numbers
Exact equivalences have an unlimited
number of significant figures.
There are exactly 3 feet in exactly 1 yard.
Therefore the “3” can be 3 or 3.0 or 3.00 or 3.000 etc.
and the “1” can be 1 or 1.0 or 1.00 or 1.000 etc. !
The same is
true for:



Scientific notation is a way of expressing
really big numbers or really small
numbers.
For very large and very small numbers,
scientific notation is more concise.
Every number written in scientific notation
has two basic parts.
• The first part is always a decimal number between
1.00 and 9.99…
• The second part is 10 times some exponent
N x 10x




Place the decimal point so that there is one non-zero digit
to the left of the decimal point.
Count the number of decimal places the decimal point
has “moved” from the original number. This will be the
exponent on the 10.
If the original number was less than 1, then the exponent
is negative. If the original number was greater than 1,
then the exponent is positive.
Example:
• Given: 289,800,000
• Start with: 2.898
• Decimal needs to move 8 places to the right
• Answer: 2.898 x 108






Simply move the decimal point to the
right for positive exponent 10.
Move the decimal point to the left for
negative exponent 10. (Use zeros to fill in
places.)
Example:
Given: 5.093 x 106
Move: 6 places to the right (positive)
Answer: 5,093,000

The exponent on the 10 tells you which
direction to move the decimal and how
many times it should be moved.
• POSITIVE EXPONENT means move RIGHT
• NEGATIVE EXPONENT means move LEFT


A standard notation number LOWER
than 1 means NEGATIVE exponent
A standard notation number GREATER
than 1 means POSITIVE exponent