Scientific Notation

What is Scientific Notation?

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

It is most often used in “scientific” calculations where the analysis must be very precise.

Why use scientific notation?

For very large and very small numbers, these numbers can be converted into scientific notation to express them in a more concise form.

Numbers expressed in scientific notation makes it easier to solve problems with big and small numbers.

Scientific notation consists of two parts:

A number between 1 and 10

A power of 10

N x 10x

Are the following in scientific notation?

Changing standard form to scientific notation.

To change standard form to scientific notation…

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

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

Continued…

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

When changing from Standard Notation to Scientific Notation:

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 = 3.489 x 105

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

.0000000672 = 6.72 x 10-8

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

The Distance From the Sun to the Earth

93,000,000

Step 1

Move decimal left Leave only one number in front of

decimal

Step 2

Write number without zeros

Step 3

Count how many places you moved decimal

Make that your power of ten

The power often is 7 becausethe decimalmoved 7 places.

93,000,000 --- Standard Form

9.3 x 107 --- Scientific Notation

Practice Problem

1) 98,500,000 = 9.85 x 10?

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

3) 279,000,000 = 2.79 x 10?

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

Write in scientific notation. Decide the power of ten.

9.85 x 107

6.41 x 1010

2.79 x 108

4.2 x 106

More Practice Problems

1) 734,000,000 = ______ x 108

2) 870,000,000,000 = ______x 1011

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

On these, decide where the decimal will be moved.

1) 7.34 x 1082) 8.7 x 1011

3) 9 x 1010

Complete Practice Problems

1) 50,0002) 7,200,0003) 802,000,000,000

Write in scientific notation.

1) 5 x 104 2) 7.2 x 106 3) 8.02 x 1011

Example 1

Given: 289,800,000 Use: 2.898 (moved 8 places) Answer: 2.898 x 108

Example 2

Given: 0.000567 Use: 5.67 (moved 4 places) Answer: 5.67 x 10-4

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#2

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 102

5.673 x 103

Changing scientific notation to standard form.

To change scientific notation to standard form…

Move the decimal point to the right for positive exponent 10.

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

(Use zeros to fill in places.)

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.

Scientific Notation to Standard Form

Move the decimal to the right

3.4 x 105 in scientific notation

340,000 in standard form

3.40000 --- move the decimal

Example

Given: 5.093 x 106

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

Example

Given: 1.976 x 10-4

Answer: 0.0001976 (moved 4 places to the left)

Write in Standard Form

6.27 x 106

9.01 x 104

6,270,000 90,100

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

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Guided PracticeHomework: Practice