SCIENTIFIC NOTATION DAY 1

• Learn Vocabulary Terms

• Identify Vocabulary terms in problems

• Understand why Scientific Notation is used

• Identify numbers written in Scientific notation & be able to explain why or why not

SCIENTIFIC NOTATION VOCABULARY

Scientific Notation: A way of expressing very large or very small numbers more easily using a power of 10

EX: 35,700 = 3.57 x 104

Standard Form: The “normal” regular way we write a numberEX: 35,700

SCIENTIFIC NOTATION VOCABULARY

Finite decimal: every whole number EX: 5, 78, 90 (any number between 1 & 9)

Leading digit: the leftmost digit : single, NON-ZERO number to the left of the decimal EX: 6.5 9.0 2.34

Order of The exponent used to magnitude: show the power (magnitude of 10)

It basically tells us how many times to move the decimal left or right.

EX: 105 = 1.00000

http://www.mathsisfun.com/numbers/scientific-notation.html

HOW DO I KNOW IF IT’S SCIENTIFIC NOTATION?

1) Must be written as a PRODUCT (X’s) EX: 3.6 x 103

2) The LEADING DIGIT must to the left of the decimal and be a WHOLE number between 1 & 9

EX: 3.6 x 103

3) There must be a order of magnitude (power of 10)

EX: 3.6 x 103

EXIT TICKET

• IDENTIFY : Leading digit Order of magnitude Product sign

7.8 x 106

SCIENTIFIC NOTATION DAY 2 & 3

• Identifying large vs. small numbers by the placement of the zeros.

• Using zero placement to tell us which direction the decimal is moved from the leading digit

• Identify if the power of 10 is positive or negative by the zeros

• Know why we use it

DO NOW

WHICH NUMBER IS THE SMALLER NUMBER &WHICH NUMBER IS THE LARGER NUMBER?

0.000000089 OR 8,000,000

BE PREPARED TO EXPLAIN/SHARE YOUR CHOICES.

SCIENTIFIC NOTATION BASICS

• Scientific Notation is a way of expressing very large or very small numbers in an easier way.

Large numbers often have MANY zeros at the end. EX: 450,000,000

Small numbers have the zeros at the beginning. EX: 0.000000032

VERY SMALL OR VERY LARGE

• Identify each number as very small or very large:

1) 0.000015 SMALL LARGE

2) 6,000,000 SMALL LARGE

3) 0.00000901 SMALL LARGE

USE/THINK ABOUT WHAT YOU ALREADY KNOW…

• What do you already know about the placement of these zeros?

• What does the direction (left; before OR right; after) they tell us about the numbers?

• HINT: Think about the number line or the decimal place value chart

WE KNOW……

*ALL of these will help you understand SCIENTIFIC NOTATION!!!

DO NOW1) Please write HW in your planners

2) With the people at your tables, complete the review sheet on your desks.

REVIEW

Vocabulary: Match the term with its definition.

____large numbers A) have zeros at the beginning

____ leading digit B) exponent that shows power of 10

____ order of C) have zeros at the end magnitude

____ small number D) leftmost digit : single, NON-ZERO number to the left of the decimal

Use the expression below to answer the questions: 7.98 x 10 6

The 7 is called the _________________

10 6 is the ______________

The “x” is the _____________

WORD BANKPRODUCT ORDER OF MAGNITUDE leading digit

IDENTIFY which is NOT written in scientific notation and give a reason why

06.9 x 103 9.7 x 52

7.89 x 104

Identify each number as very small or very large:

1) 0.000025 SMALL LARGE

2) 9,000,000 SMALL LARGE

3) 0.00000745 SMALL LARGE

Writing numbers in Scientific Notation

• Identifying large vs. small numbers by the placement of the zeros.

• Using zero placement to tell us which direction the decimal is moved from the leading digit

• Identify if the power of 10 is positive or negative by the zeros

How to Do it:Writing large numbers in Scientific Notation

• To figure out the power of 10, think "how many places do I move the decimal point?“

• If the number is 10 or greater, the decimal point has to move to the left, and the power of 10 will be positive; large number

VIDEO

http://learnzillion.com/lessons/1177-write-large-numbers-in-scientific-notation

EXAMPLE: Write 4,250,000,000 in scientific notation

4.250000000.

4.250000000. 9 places

4.25 x 109

Move the decimal so that only 1 digit is to the left of the decimal

Count the number of spaces thatthe decimal has to be moved to theRIGHT.

Write the number WITHOUT endingthe zeros, & multiply by the correct power of 10

Let’s PRACTICE

Write each number in scientific notation:

1) 68,000

2) 73,280,000

How to Do it:Writing Small numbers in Scientific Notation

• To figure out the power of 10, think "how many places do I move the decimal point?“

• If the number is smaller than 1, the decimal point has to move to the right, so the power of 10 will be negative; small number

VIDEO http://learnzillion.com/lessons/1255-write-small-numbers-in-scientific-notation

EXAMPLE: Write 0.0000000425 in scientific notation

0.00000004.25

0.00000004.25 8 places

4.25 x 10-8

Move the decimal so that only 1 NON ZERO digit is to the left of the decimal

Count the number of spaces thatthe decimal has to be moved to theLEFT.

Write the number WITHOUT beginningthe zeros, & multiply by the correct power of 10 AND use a NEGATIVEexponent to move the decimal to the left.

Let’s PRACTICE

Write each number in scientific notation:

1) 0.0038

2) 0.0000004

Check!

After putting the number in Scientific Notation,just check that:

• The "digits" part is between 1 and 10 (it can be 1, but never 10)

• The "power" part shows exactly how many places to move the decimal point

EXIT TICKET

Write the following in scientific notation:

1) 53,000 _______________

2) 0.0082 _______________

ORIGINAL NUMBER PLACE DECIMAL & MOVE IN CORRECT DIRECTION FINAL ANSWER

420,000 4.2 0 0 0 0 4.2 x 105

0.002 0.0 0 2. 2 x 10-3

30,000,000

0.00037

804,000,000

13,060,000,000,000

0.0000506

0.000000005507

45,000,000

5,840,000

Name:_______________________ Date:_____________________CLASSWORK M1L9 BASIC SCIENTIFIC NOTATION

NEGATIVE POSITIVE

Write each number in scientific notation:

LEFT RIGHT

:

SCIENTIFIC NOTATION DAY 4 & 5

• Use knowledge of decimal movement & scientific notation to convert

• Convert FROM scientific notation TO standard form with positive & negative exponents

HOW TO USE THE CALCULATOR

1) On2) Clear3) Enter the standard form number4) Press blue “2nd “ key5) Press “DRG” ( SCI/ENG)6) Using the right/left arrow keys choose: “FLO” for standard form “ SCI” for scientific notation*if you want to go back to choose another form

repeat steps 5 and 6 and then press enter twice

http://www.youtube.com/watch?v=BW55IniDb2g&list=PL698BE8091CA9C622

SCIENTIFIC NOTATION VOCABULARY

Scientific Notation: A way of expressing very large or very small numbers more easily using a power of 10

EX: 35,700 = 3.57 x 104

Standard Form: The “normal” regular way we write a numberEX: 35,700

CONVERTING FROM SCIENTIFIC NOTATION TO STANDARD FORM

It’s EASY!!!!

ALL you do is work BACKWARDS…

SMARTEXCHANGE

EXAMPLE: WITH A POSITIVE EXPONENT Write 7.035 X 106 in STANDARD FORM

The exponent is a 6 and it is positive

Move the decimal 6places to the RIGHT

7.035000. 6 places

7,035,000

• Study the exponent

• Move the decimal point the Correct number of places to the right

• Add any necessary zeros at the END of the number as place holders

• Write the number in standard form

http://www.youtube.com/watch?v=8bUvkPYXjco

LETS PRACTICESCIENTIFIC NOTATION

DECIMAL MOVEMENT

STANDARD FORM

5.3 x 104

9.24 x 108

1.205 x 105

EXAMPLE: WITH A NEGATIVE EXPONENTWrite 4.16 x 10-5 In STANDARD FORM

The exponent is a -5 and it is negative

Move the decimal 5places to the LEFT

0.00004.16. 5 places

0.0000416

• Study the exponent

• Move the decimal point the correct number of places to the left

• Add any necessary zeros at the BEGINNING to fill up to the decimal point

• Write the number in standard form

http://www.youtube.com/watch?v=8bUvkPYXjco

LETS PRACTICESCIENTIFIC NOTATION

DECIMAL MOVEMENT

STANDARD FORM

7.1 x 10-4

5.704 x 10-6

8.65 x 10-2

EXIT TICKETSuppose the table below displays data for the Top prime-time television shows for a given week the year. Complete the empty columns in table by converting the number of households into either scientific notation OR standard form.

NAME OF SHOW NUMBER OF HOUSEHOLDSSTANDARD FORM

NUMBER OF HOUSEHOLDSSCIENTIFIC NOTATION

The Voice 15,553,000

Duck Dynasty 1.4623 x 107

The Simpsons 0.0865

HOMEWORK

• SCIENTIFIC NOTATION PUZZLE

http://www.youtube.com/watch?v=QarMTT5YweQ&list=PL698BE8091CA9C622