SCIENTIFIC NOTATION

CHAPTER 4 SECTION 3

MTH 10905Algebra

Convert Numbers to and from Scientific Notation

Numbers written in Scientific notation is written as a number greater than or equal to 1 and less than 10, (1 £ a < 10), Multiplied by a power of 10.

Convert Numbers to and from Scientific Notation

6000 = 6 x 103

6,160,000,000 = 6.16 x 109

0.0000001 = 1.0 x 10-7

Examples of numbers

in scientific notation

To Write a Numberin Scientific Notation

Move the decimal point in the right of the first nonzero digit. ≥1 and <10

Count the number of decimal places you moved the original number.

If the original number is 10 or greater then count is positive.

If the original number is <1 then count is negative.

Multiple step 1 by 10 to the power of your count in step 2

Express in Scientific Notation

Example:

0.0000786

7.86 x 10-5

Example:

1,340,000

1.34 x 106

Convert a Number from Scientific Notation to Decimal Form

Observe the exponent in the power of 10

If exponent is positive ≥1 and <10 move the decimal to the right. May have to add zero’s

If exponent is 0. Drop the factor 100 because that equals 1. Do NOT move the decimal.

If exponent is negative <1 move decimal to the left. May have to add decimals

Express in Decimal Form (without exponents)

Example: 5.23 x 10-2

5.23 x 1/100Move 2 place to the left0.0523

Example: 3.201 x 1010

3.201 x 10,000,000,000Move 10 places to the

right32,010,000,000

Scientific Notation with a Coefficient of 1

The metric system is used in every westernized nation except the United States

kilograms, milligrams, gigabytes

1 millimeter (m) = 10-3 or 1/10001 megagram (M) = 106 or 1,000,000

See other in table on page 253

Scientific Notation with a Coefficient of 1

Remember that we assume 1 when no numerical coefficient exists

Example:Write 76 millimeter without the metric prefix.

76 x 10-3 move three places to the left0.076 meters

Scientific Notation with a Coefficient of 1

Example:Write 472.1 Kilometers without the metric prefix.

472.1 x 103 move three places to the right472,100 meters

Example:Write 12.5 nanometers without the metric prefix.

12.5 x 10-9 move three places to the left0.0000000125 meters

Calculation using Scientific Notation

Use the rules of exponents

Example: Multiply and write in decimal form.

(2.8 x 107)(3.0 x 10-3)

(2.8)(3.0)(107)(10-3)8.4 x 107+(-3) 8.4 x 104

Move the decimal place 4 places to the right84,000

Calculation using Scientific Notation

Example: Divide and write in Scientific Notation.

4)7()3(7

3

7

3

10 0.210 0.210

10

8.2

6.5

10 8.2

10 6.5

Calculation using Scientific Notation

Example: The weight of the Earth is 5.972 x 1024 kg. The weight of the Earth’s Moon is 7.35 x 1022 kgA. How much greater is the weight of the Earth than the weight

of its Moon?B. How many times greater is the weight of the Earth than the

weight of its moon?

22

22

22

24

597.20 10

7.35 10

589.85 10

Move the decimal back to the left 2

Move the exponent back to 24

5.8985 10 kg

greater times25.81

100 812517.

10 812517.

10 812517.

10

10

35.7

972.5

10 35.7

10 972.5

2

2224

22

24

22

24

A. B.

Remember

The numerical value preceding the base must be greater than or equal to 1 but less than 10

The sign of the exponent on the base indicates which direction to move the decimal point. Negative moves left Positive moves right

HOMEWORK 4.3

Page 257#17, 18, 21, 31, 35, 65, 69, 72