Scientific Notation

0806.2.1    Recognize and use 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.2.1 x 1023

When using Scientific Notation, there are two kinds of exponents: positive and negative

Positive Exponent:2.35 x 108

Negative Exponent:3.97 x 10-7

When changing scientific notation to standard notation, the exponent tells you how you should move the decimal:

With a positive exponent, move the decimal to the right:

4.08 x 103 = 4 0 8

Don’t forget to fill in your zeroes!

When changing scientific notation to standard notation, the exponent tells you how you should move the decimal:

With a negative exponent, move the decimal to the left:4.08 x 10-3 = 4 0 8

Don’t forget to fill in your zeroes!

An easy way to remember this is:

• If an exponent is positive, the number gets larger, so move the decimal to the right.

• If an exponent is negative, the number gets smaller, so move the decimal to the left.

The exponent also tells how many spaces to move the decimal:

4.08 x 103 = 4 0 8 In this problem, the exponent is +3, so the decimal moves 3 spaces to the right.

The exponent also tells how many spaces to move the decimal:

4.08 x 10-3 = 4 0 8

In this problem, the exponent is -3, so the decimal moves 3 spaces to the left.

Try changing these numbers from Scientific Notation to Standard Notation:

1) 9.678 x 104

2) 7.4521 x 10-3

3) 8.513904567 x 107

4) 4.09748 x 10-5

96780

.0074521

85139045.67

.0000409748

When changing from Standard Notation to Scientific Notation:

1) First, move the decimal after the first whole number:

3 2 5 8

123

3

2) Second, add your multiplication sign and your base (10).

3 . 2 5 8 x 10

3) Count how many spaces the decimal moved and this is the exponent. 3 . 2 5 8 x 10

When changing from Standard Notation to Scientific Notation:

4) See if the original number is greater than or less than one.– If the number is greater than one, the

exponent will be positive.

348943 = 3.48943 x 105

– If the number is less than one, the exponent will be negative.

.0000000672 = 6.72 x 10-8

Try changing these numbers from Standard Notation to Scientific Notation:

1) 9872432

2) .0000345

3) .08376

4) 5673

9.872432 x 106

3.45 x 10-5

8.376 x 10-2

5.673 x 103

Scientific Notation Math

Multiplication- multiply the numbers, add the indices

1.2 x 104 multiplied by 5 x 106 =

Division- divide the numbers, subtract the indices

5.5 x 108 divided by 1.1 x 102 =

(For all operations reconvert answers to full scientific notation)

On a Calculator• Locate these buttons: , , , • Scientific Standard given 1.2 x 105

– 1.2 x 10 5 = 120,000

– 1.2 5 = 120,000

• Standard Scientific given 120,000– 120,000 = select Sci =

– To undo: select Flo =

^ LOG

10X

2nd DRGSci/Eng

^

2nd LOG

10X

DRGSci/Eng

DRGSci/Eng

Convert the following numbers between standard form and scientific notation:329

700,000

20090

0.000034

0.01023

123.4

45.607

1.7 x 103

2.4503 x 105

7.9 x 1011

2.8 x 10-3

7.45 x 10-1

2.3 x 10-7

Convert the following numbers/sums into correct scientific notation:

35.9 x 103

556.67 x 104

22.7 x 10-3

0.0348 x 10-1

1845 x 105

123.4 x 1023

0.00345 x 107