Transcript Metric Conversion and Scientific Notation

Monday, September 21, 2015
Tuesday, September 22, 2015
Unit Question
How do we “do” science?
Guiding Question / I will be able to do metric conversions and scientific notation.
Learning Target
Warm-up
Why is the metric system easier than the standard/English
system?
Counts by 10!
Agenda
1. Metric Notes
2. Conversions Worksheets
Homework
1. Quiz this Friday! No notes.
2. TEST Next week! Be able to use equipment. Open note.
Quiz Retakes?
• Still closed note—until AT starts you’ll be taking them in the
hall
• Today or next class are your options this week: you’ve got 1
chance and has to be done within a week.
• Finish your worksheets today, want to retake? See me!
• It is a different quiz…you should still study!
• Your score:
•
•
•
•
•
7/7 = 100% A
6/7 = 85% B
5/7 = 71% C4/7 = 57% Probably do retakes
3/7 = 42% Definitely do retakes
Metric System
“I’m ten times better than the Standard system of
measurement!”
Let’s do some review work before
we begin.
Do the following calculations
230 x 10 = 2300
4.5 x 10 = 45
4500 x 100 = 450000
97.45 x 100 = 9745
5780  10 = 578
348  100 = 3.48
123.5  10 = 12.35
21.6  100 = .216
8.465  100 = .08465
Nice Job!
If you can multiply
& divide by 10 (or
any power of 10),
then the metric
system will be easy
for you.
Converting Metric
Units
How many centimeters is in 5 meters?
Metric Prefixes
Prefix
Abbreviation
Definition
giga
G
10 or 1,000,000,000 (Billions)
mega
M
10 or 1,000,000 (Millions)
kilo
k
10 or 1,000 (Thousands)
hecto
h
10 or 100 (Hundreds)
deka (or, deca, depending on
your textbook)
da
10 or 10 (Tens)
deci
d
1/10 or 0.1 (Tenth)
centi
c
1/100 or 0.01 (Hundredth)
milli
m
1/1000 or 0.001 (Thousandth)
micro
µ (Greek
letter mu)
10 or 0.000001 (Millionth)
9
6
3
2
1
-6
These are on the back of your notes. Star, highlight, or
otherwise mark the yellow ones. These are the most
common prefixes, and the ones we’ll use in class.
What is the order of the metric system?
• King Henry’s Daughter Bakes Delicious Chocolate Muffins
• King: Kilo
• Henry’s: Hecto
• Daughter: Deca
• Bakes: Base (m, L, g)
Do you want
• Delicious: Deci
to write this
• Chocolate: Centi
down?
• Muffins: Milli
Writing Metric abbreviations
• Prefix plus base unit
• Kiloliter = kL
• Millimeter = mm
• Meter = m
???
Just one letter?
That means it’s your base unit!
Converting Units:
THE Golden Rule
• When going from a
big unit to a small
unit:
• MULTIPLY!!
• Or move decimal
place to the right;
add zeros as needed
as place holders.
• When going from a
small unit to a big
unit:
• DIVIDE!!
• Or move decimal
place to the left; add
zeros as needed as
place holders.
The Ladder Method
• Each step multiply or divide by 10
• Or each step move the decimal one place to the left or to the
right
Convert 2.5L to mL
We start here, with L
We end here,
with mL
How many steps does it take to
get from L, our basic units, to mL?
Convert 2.5L to mL
How many steps did we take?
3 steps
Convert 2.5L to mL
How many decimal places do we move?
3 places
Convert 2.5L to mL
Which direction did we move?
To the Right
Convert 2.5L to mL
Which direction does the decimal go?
To the Right
What’s that look like?
•2.5 0 0
Convert 2.5L to mL
What do our numbers look like?
2.5L a25dLa250cLa2500mL
2.5L=2500mL
So now, to go left…
Convert 5000 m to Km
So now, to go left…
3
Count your steps
And move your decimal
5.0km 50.0hm 500.0Dm 5000.0m
5000.0m = 5.0km
Now you try:
•
•
•
•
•
7,000
7 km = __________
m
600
6 g = __________
cg
9150
9.15 kL = __________
L
6250000
6.25 kg = __________
mg
1420
14.2 m = __________
cm
SCIENTIFIC NOTATION
How wide is our universe?
210,000,000,000,000,000,000,000 miles
(22 zeros)
This number is written in decimal
notation. When numbers get this
large, it is easier to write them in
scientific notation.
Check out this website!
Scientific Notation
Scientific notation is a shorter way
to write very long numbers.
Scientific Notation is based on
powers of the base number 10.
• The number 123,000,000,000 in scientific notation is written
as: 1.23 x 1011
• The first number 1.23 is called the coefficient.
• It must be greater than or equal to 1 and less than 10.
• The second number is called the base. It must always be 10.
The base number 10 is always written in exponent form.
• In the number 1.23 x 1011 the number 11 is referred to as the
exponent or power of ten.
Scientific Notation
• This number is in scientific notation:
1.23 x 1011
• This number is NOT in scientific notation:
12.3 x 1011
• What’s the difference?
• The DECIMAL place!
• To be in scientific notation there can only be ONE number to
the LEFT of the decimal. That number must be 1-9.
Getting into scientific notation
• Put the decimal after the first digit and drop the end zeroes.
• In the number 123,000,000,000 The coefficient will be 1.23
• To find the exponent count the number of places from the
decimal to the end of the original number.
• In 123,000,000,000 there are 11 places. Therefore we write
123,000,000,000 as: 1.23 x 1011
• For small numbers we use a similar approach. Numbers
smaller than 1 will have a negative exponent.
• A millionth of a second is: 0.000001 sec. OR 1.0 x10-6
Getting out of Scientific
Notation
• What’s the x 10exponent mean?
• That exponent is how many places the decimal moves
over.
• 1.23 x 1011 the decimal moves over 11 places to the
RIGHT, making a BIG number: 1,230,000,000
• What about x 10-exponent ?
• With a NEGATIVE exponent, it’s still how many places
you move, but your direction changes.
• 1.23 x 10-11 the decimal moves over 11 places to the
LEFT, making a SMALL number: 0.0000000000123
Scientific Notation
• What If I need to turn a number into scientific notation?
• Start moving the decimal!
• 1,230,000
• Where is the decimal now?
• Where should it be?
• 1 230000
• How many places did it move?
• 1230000
6
• That number of places becomes my superscript.
• What’s my scientific notation?
• 1.23 x 106
Write the width of the universe in
scientific notation.
210,000,000,000,000,000,000,000 miles
Where is the decimal point now?
After the last zero.
Where would you put the decimal to
make this number be between 1 and 9?
Between the 2 and the 1
2.10,000,000,000,000,000,000,000.
How many decimal places did you move
the decimal?
23
When the original number is more than 1,
the exponent is positive.
The answer in scientific notation is
2.1 x 1023
1) Express 0.0000000902 in
scientific notation.
Where would the decimal go to make the
number be between 1 and 9?
9.02
The decimal was moved how many
places?
8
When the original number is less than 1,
the exponent is negative.
9.02 x 10-8
2) Express 1.8 x 10-4 in decimal notation.
0.00018
3) Express 4.58 x 106 in decimal
notation.
4,580,000
Example Problems
6
5.8763
x
10
1) 5,876,300 =
-5
1.52
x
10
2) 0.0000152 =
3) 3.268 x
4)
4
10
3.76 x
= 32680
-3
10
= .00376
Metric Conversion & Scientific
Notation Practice
• Both worksheets should be
completed in class
• I want to check them off when you
finish, but:
• You can keep them until Friday to
study for the quiz and use as
reference.
• Don’t lose these!
Keys
• Scientific Notation Key
• Metric key
Exit Question
• How many decimeters are in 1.5 meters?
• 15 dm
• Convert 1.42 x 10-3 to a normal number?
• .00142