WARM UP Algebra 21/22 March 2012

Solving Equations HandoutDo 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

objectivesStudents 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 FridayHomework due Fridaypg. 357: 1- 4, 11, 15pg. 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)7x42)10x43)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 RememberFrom zero to the right the numbers get BIGGER .

From zero to the left the numbers get SMALLER.

Numbers On a Number Line

Numbers On a Number Line 1)

2)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

In science, we deal with some very In science, we deal with some very LARGELARGE numbers: numbers:

1 mole = 6020000000000000000000001 mole = 602000000000000000000000

In science, we deal with some very In science, we deal with some very SMALLSMALL numbers: numbers:

Mass of an electron =Mass of an electron =0.000000000000000000000000000000091 kg0.000000000000000000000000000000091 kg

Scientific NotationScientific Notation

Imagine the difficulty of calculating the Imagine the difficulty of calculating the mass of 1 mole of electrons!mass of 1 mole of electrons!

0.000000000000000000000000000000091 kg0.000000000000000000000000000000091 kg x 602000000000000000000000x 602000000000000000000000

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Scientific Notation:Scientific Notation:

A way of representing very large A way of representing very large or very small numbers in the or very small numbers in the

form: form: aa x 10 x 10n INTEGERn INTEGER

aa is a number betweenis a number between 11 andand 10 10 (Yes decimal numbers such as (Yes decimal numbers such as 0.7 or 2.5 or 7.7).0.7 or 2.5 or 7.7).

nn is an integer (is an integer (whole numbers like – 2 whole numbers like – 2 or 11 but decimal).or 11 but decimal).

TIMES

In other words:In other words:Scientific notation expresses a Scientific notation expresses a number in the form:number in the form:

a a x 10x 10nn

1 1 aa 10 10

n is an n is an integerinteger

CLASSWORK

Do NowIdentify “a” and “n” from each expressions.

1) 2) 3)

a= _______ a= _______ a=_________n = ______ n=________ n=_________

CLASSWORK

Do Now: Investigation: A Scientific Quandary Page 355 Steps 1 and 2 BE READY TO SHARE

.2 500 000 000

Step #1: Insert an understood decimal pointStep #1: Insert an understood decimal point

Step #2: Decide where the decimal must end Step #2: Decide where the decimal must end up so that one number is to its leftup so that one number is to its left

Step #3: Count how many places you bounce Step #3: Count how many places you bounce the decimal pointthe decimal point

123456789

Step #4: Re-write in the form Step #4: Re-write in the form M x 10M x 10nn

SCIENTIFIC NOTATION FOR LARGE NUMBERS

2.5 x 102.5 x 1099

The exponent is the number of places we moved the decimal.

LET DO ONE TOGETHERWrite the following number in scientific notation.Two-hundred-and eighty million280, 000, 000

answer: 2.8 x 108

0.00005790.0000579

Step #2: Decide where the decimal must end Step #2: Decide where the decimal must end up so that one number is to its leftup so that one number is to its left

Step #3: Count how many places you bounce Step #3: Count how many places you bounce the decimal pointthe decimal point

Step #4: Re-write in the form M x 10Step #4: Re-write in the form M x 10nn

1 2 3 4 5

SCIENTIFIC NOTATION FOR SMALL NUMBER

5.79 x 105.79 x 10-5-5

The exponent is negative because the number we started with was less than 1.

VIDEO

http://www.youtube.com/watch?v=H578qUeoBC0

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/algebra1/algebra1_01/pdf/0903.pdf

http://www.youtube.com/watch?v=H578qUeoBC0