Transcript Algebra 1- 21 March 2012 Properties of - Shope-Math

WARM UP Algebra 21/22 March 2012
Solving Equations Handout
Do FOUR problems, showing all steps.
Show your CHECK by substituting back into
the original.
- get a calculator
- put your text and binder on your desk
objectives
Students will be able to write large numbers in
scientific notation and in standard form.
Students will take notes, participate in class
discussion and use think-pair-share.
Homework due Friday
pg. 357: 1- 4, 11, 15
Review exponents
5x5 = 51∙x2 = 5∙x∙x∙x∙x∙x
(5x)5 = (5x)(5x)(5x)(5x)(5x)
How are they different?
PRACTICE- expand:
1)7x4
2)10x4
3)4x7
Working with BIG numbers
Meredith is doing a report on stars and wants to
estimate the total number of stars in the
universe. She reads that astronomers estimate
there are at least 125 billion galaxies in the
universe. An encyclopedia says that the Milky
Way, Earth’s galaxy, is estimated to contain more
than 100 billion stars. Estimate the total
number of stars in the universe.
Things to Remember
From zero to the left the numbers
get SMALLER.
From zero to the right the numbers
get BIGGER .
Numbers On a Number Line
1)
2)
Numbers On a Number Line
Place the following numbers on the number line.
a) 0.9
b) 2.7
c) 5.56
d) 9.9
e) 7.7
3) Write down two very, very large numbers.
4) Write down 2 very, very small positive (+)
numbers.
5) List (write down) 15 numbers between 1 and 10.
Scientific
Notation
Scientific Notation
In science, we deal with some very
LARGE numbers:
1 mole = 602000000000000000000000
In science, we deal with some very
SMALL numbers:
Mass of an electron =
0.000000000000000000000000000000091 kg
Imagine the difficulty of calculating the
mass of 1 mole of electrons!
0.000000000000000000000000000000091 kg
x 602000000000000000000000
??????????????????????????????????
Scientific Notation:
A way of representing very large
or very small numbers in the
form:
a x 10n
INTEGER
TIMES
 a is a number between 1 and 10
(Yes decimal numbers such as 0.7 or 2.5 or 7.7).
 n is an integer (whole numbers like – 2
or 11 but decimal).
In other words:
Scientific notation expresses a
number in the form:
ax
1  a  10
n
10
n is an
integer
CLASSWORK
Do Now
Identify “a” and “n” from each expressions.
1)
2)
a= _______
n = ______
a= _______
n=________
3)
a=_________
n=_________
CLASSWORK
Do Now:
Investigation: A Scientific Quandary
Page 355 Steps 1 and 2
BE READY TO SHARE
SCIENTIFIC NOTATION FOR LARGE
NUMBERS
2 500 000 000 .
9
8
7
6
5
4
3
2
1
Step #1: Insert an understood decimal point
Step #2: Decide where the decimal must end
up so that one number is to its left
Step #3: Count how many places you bounce
the decimal point
Step #4: Re-write in the form M x 10n
2.5 x
9
10
The exponent is the
number of places we
moved the decimal.
LET DO ONE TOGETHER
Write the following number in scientific notation.
Two-hundred-and eighty million
280, 000, 000
answer:
2.8 x 108
SCIENTIFIC NOTATION FOR
SMALL NUMBER
0.0000579
1
2
3
4
5
Step #2: Decide where the decimal must end
up so that one number is to its left
Step #3: Count how many places you bounce
the decimal point
Step #4: Re-write in the form M x 10n
5.79 x
-5
10
The exponent is negative
because the number we started
with was less than 1.
VIDEO
http://www.youtube.com/watch?v=H578qUeo
BC0
Example: Large numbers
• Given: 289,800,000
Use: 2.898 -- between 1 and 10
(moved 8 places)
Answer: 2.898 x 108
Example 2
• Given: 0.000567
• Use: 5.67 (moved 4 places)
• Answer: 5.67 x 10-4
Use: 5.67 - a number between 1 and 10
(moved 4 places)
Answer: 5.67 x 10-4
Negative because it is a small number
Example 3
• Given: 5.093 x 106
• HOW? ADD 6 decimal places to 5.093
Answer: 5,093,000
(moved 6 places to the right)
positive exponent means
BIGGER NUMBER
Example 4
• Write in scientific notation
800,000 x 104
• Rewrite 800,000 as 8.0 x 105
• 800,000 x 104 = 8.0 x 105 x 104
= 8.0 x 105+4
= 8.0 x 109
LET’S DO ONE TOGETHER
• Given: 0.000567
• Answer: 5.67 x 10-4
Use: 5.67 (moved 4 places)
Answer: 5.67 x 10-4
Let’s do one together.
Do Handout 6.4
Do your work on a separate paper if you need
more room.
Be ready to show your work to the class.
CLASSWORK paper- debrief
SUMMARY:
1)Write five things you learned or relearned
today.
2) Make up a question someone might ask
about exponents.
Glencoe practice
http://www.glencoe.com/sec/math/algebra/al
gebra1/algebra1_01/pdf/0903.pdf
http://www.youtube.com/watch?v=H578qUeo
BC0