Scientific Notation

Scientific Notation

Scientific Notation: a short-hand way of writing large numbers or small numbers without writing all of the zeros.

The Distance From the Sun to the Earth

93,000,000

Step 1

• 1) Rewrite the number as a number less than 10 but at least 1.

9.3 is less than 10, but at least one

• Write number without zeros

Then…..

• Count how many places you moved decimal

• Make that your power of ten

Step 2

•93,000,000 --- Standard Form

•9.3 x 107 --- Scientific Notation

Standard v Scientific

Example 1

• Convert to Scientific Notation• Given: 289,800,000

• Use: 2.898• Answer:

Why is the exponent positive?

2. 898 x 108

Practice Problem

1) 0.0985 = 9.85 x 10?

2) 64,100,000,000 = 6.41 x 10?

3) 0.00279 = 2.79 x 10?

4) 4,200,000 = 4.2 x 10?

Write in scientific notation. Decide the power of 10

9.85 x 10-2

6.41 x 1010

2.79 x 10-3

4.2 x 106

More Practice Problems

1) 734,000,000 = ______ x 108

2) 0.00072 = ______x 10-4

3) 90,000,000,000 = _____ x 1010

On these, decide where the decimal will be moved.

1) 7.34 x 108 2) 7.2 x 10-4 3) 9 x 1010

Complete Practice Problems

1) 50,000

2) 0.005

3) 802,000,000,000

Write in scientific notation.

1) 5 x 104 2) 5.0 x 10-3 3) 8.02 x 1011

Scientific Notation to Standard Form

Step 1: Determine the sign of the power of 10.

Step 2: Move the decimal point according to the power of 10.

Scientific Notation to Standard Form

3.4 x 105 in scientific notation

340,000 in standard form

3.40000 --- move the decimal

Example 1

Example 2

• Convert to Standard Notation

• Given: 5.093 x 10-6

• Answer: (move 6 places to the right)

0.000005093

Write in Standard Form

1) 6.27 x 106

2) 9.01 x 104

3) 5.98 x 10-3

4) 9.0 x 100