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Page 1: Scientific Notation

Scientific Notation

0806.2.1    Recognize and use scientific notation.

Page 2: 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

Page 3: Scientific Notation

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

Page 4: Scientific Notation

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!

Page 5: Scientific Notation

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!

Page 6: Scientific Notation

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.

Page 7: Scientific Notation

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.

Page 8: Scientific Notation

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.

Page 9: Scientific Notation

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

Page 10: Scientific Notation

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

Page 11: Scientific Notation

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

Page 12: Scientific Notation

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

Page 13: Scientific Notation

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)

Page 14: 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

Page 15: Scientific Notation

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

Page 16: Scientific Notation

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


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