Transcript Write the number in scientific notation.

METRIC
CONVERSIONS
LADDER METHOD
T. Trimpe 2008 http://sciencespot.net/
Ladder Method
1
2
KILO
1000
Units
3
HECTO
100
Units
DEKA
10
Units
DECI
0.1
Unit
Meters
Liters
Grams
How do you use the “ladder” method?
1st – Determine your starting point.
2nd – Count the “jumps” to your ending point.
3rd – Move the decimal the same number of
jumps in the same direction.
CENTI
0.01
Unit
MILLI
0.001
Unit
4 km = _________ m
Starting Point
Ending Point
How many jumps does it take?
4. __. __. __. = 4000 m
1
2
3
Conversion Practice
Try these conversions using the ladder method.
1000 mg = _______ g
1 L = _______ mL
160 cm = _______ mm
14 km = _______ m
109 g = _______ kg
250 m = _______ km
Compare using <, >, or =.
56 cm
6m
7g
698 mg
Scientific
Notation
Scientific Notation Essential
Questions
How do I write numbers in scientific
notation?
How do I calculate with scientific notation?
When would I use scientific notation?
The table shows relationships between several powers of
10.
• Each time you divide by 10, the exponent in the
power decreases by 1 and the decimal point in the
value moves one place to the left.
• Each time you multiply by 10, the exponent in the
power increases by 1 and the decimal point in the
value moves one place to the right.
You can find the product of a number and a
power of 10 by moving the decimal point of
the number. You may need to write zeros
to the right or left of the number in order
to move the decimal point.
Additional Example 1: Multiplying by Powers of
Ten
Multiply.
A. 14  104
14.0 0 0 0
140,000
B. 3.6  10-5
0 0 0 0 3.6
0.000036
Since the exponent is a
positive 4, move the decimal
point 4 places to the right.
Since the exponent is a
negative 5, move the decimal
point 5 places to the left.
Powers of 10 are used when writing
numbers in scientific notation. Scientific
notation is a way to express numbers that
are very large or very small. Numbers
written in scientific notation are expressed
as 2 factors. One factor is a number
greater than or equal to 1. The other factor
is a power of 10.
Additional Example 2: Writing Numbers in
Scientific Notation
Write the number in scientific notation.
A. 0.00709
Think: The decimal needs to move
3 places to get a number between 1
and 10.
7.09  10-3
Think: The number is less than 1, so
the exponent will be negative.
So 0.00709 written in scientific notation is 7.09  10–3.
Additional Example 2: Writing Numbers in
Scientific Notation
Write the number in scientific notation.
B. 23,000,000,000
2.3  1010
Think: The decimal needs to
move 10 places to get a
number between 1 and 10.
Think: The number is greater
than 1, so the exponent will
be positive.
So 23,000,000,000 written in scientific notation is
2.3  1010.
SIGNIFICANT FIGURES
(SIG. FIGS)
Rules:
All non-zero #’s are significant
Some zeros are significant; others are place
holders
SIG FIGS
Only measurements have sig figs.
Counted numbers are exact
A dozen is exactly 12
A piece of paper is measured 11 inches
tall.
Being able to locate, and count significant
figures is an important skill.
ATLANTIC-PACIFIC RULE
Ask yourself: self, is there a decimal?
PACIFIC
ATLANTIC
(Present)
(Absent)
Start from LEFT
Start from RIGHT
& count all #’s from
& count all #’s from
first nonzero
first nonzero
PRACTICE MAKES PERFECT!
How many sig figs?
PRESENT
ABSENT
Start from LEFT and count all #’s from
first nonzero
Start from RIGHT and count all #’s
from first nonzero
4.001
0.0203
100.
4
3
3
4001
503000
100
4
3
1
SIG. FIGS IN SCIENTIFIC NOTATION
All #’s (excluding x 10xx) ARE significant
How many sig. figs?:
 3.2 x 103
 3.20 x 103
 Put 0.08400 in scientific notation w/ sig. figs
SIG. FIG. CALCULATIONS
Multiplication/Division
Rules:
The measurement w/ the smallest # of sig. figs
determines the # of sig. figs in answer
Let’s Practice!!!
6.221cm x 5.2cm = 32.3492 cm2
4
2
 How many sig figs in final answer???
 And the answer is….
32 cm2
ROUNDING RULES
look at the number behind the one you’re rounding.
If it is 0 to 4 don’t change it
If it is 5 to 9 make it one bigger
round 45.462 to four sig figs
to three sig figs
to two sig figs
to one sig fig