scientific notation? scientific notation is a way of expressing really big numbers or really small...

Scientific Notation?Scientific Notation?

• Scientific notation is a way of Scientific notation is a way of expressing really big numbers or expressing really big numbers or really small numbers.really small numbers.

• Use only Use only Significant FiguresSignificant Figures..

602,000,000,000,000,000,000,000602,000,000,000,000,000,000,000

6.02 X 106.02 X 102323

** Only 1 number to the left of the decimal** Only 1 number to the left of the decimal

To change standard form To change standard form to scientific notation…to scientific notation…

• Place the decimal point so that there is Place the decimal point so that there is one non-zero digit to the left of the one non-zero digit to the left of the decimal point.decimal point.

• Count the number of decimal places Count the number of decimal places the decimal point has “moved” from the decimal point has “moved” from the original number. This will be the the original number. This will be the exponent on the 10.exponent on the 10.

• If the original number was less than 1, If the original number was less than 1, then the exponent is negative. If the then the exponent is negative. If the original number was greater than 1, original number was greater than 1, then the exponent is positive.then the exponent is positive.

Power of 10Power of 10

1000 1000 10 X 10 X 10 10 X 10 X 10 10 1033

100 100 10 1022

10 10 10 1011

1 1 10 1000

0.1 0.1 10 10-1-1

0.01 0.01 10 10-2-2

1/10 X 1/10 X 1X10 = 1/101/10 X 1/10 X 1X10 = 1/1033 = 10 = 10-3-3

Larger

Smaller

Learning Check

2500 =

2.5 X 103

0.25 X 102 =

2.5 X101

0.25 X 10-2 =

2.5 X 10-3

To change scientific To change scientific notation to standard notation to standard

form…form…• Simply move the decimal point to Simply move the decimal point to

the right for positive exponent 10. the right for positive exponent 10.

• Move the decimal point to the left Move the decimal point to the left for negative exponent 10.for negative exponent 10.

(Use zeros to fill in places.)(Use zeros to fill in places.)

ExampleExample

• Given: 5.093 x 10Given: 5.093 x 1066

• Answer: Answer: 5,093,0005,093,000 (moved 6 places (moved 6 places to the right)to the right)

• Given: 1.976 x 10Given: 1.976 x 10-4-4

• Answer: Answer: 0.00019760.0001976 (moved 4 places (moved 4 places to the left)to the left)

Changing Numbers Into Scientific Notation

500,000500,000

0.000,000,0420.000,000,042

285.2285.2

0.000020.00002

83,700,00083,700,000

5.0 X 105.0 X 1055

4.2 X 104.2 X 10-8-8

2.852 X 102.852 X 1022

2 X 102 X 10-4-4

8.37 X 108.37 X 1077

Changing Numbers Out Of Scientific Notation

4 X 10-3

3.4 X 105

0.045 X 104

5.9 X 10-6

0.004

340,000

450

0.0000059

Adding and Subtracting

***Powers of 10 need to be the same.

3,200 3.2 X 103 3.2 X 103

+ 250 2.5 X 102 +0.25 X 103

3,450 3.45 X 103 3.45X 103

3.14 X 102

+ 4.13 X 103

0.314 X 103

+ 4.13 X 103

4.444 X 103

6.3 X 103

- 2.3 X 102

6.3 X 103

- 0.23 X 103

6.07 X 103

(6.6 X 10-8) + (5.0 X 10-9) =

7.1 X 10-8

(6.7 X 10-2) – (3.0 X 10-3) =

6.4 X 10-2