Scientific Notation Chapter 4 Section 3 MTH 10905 Algebra Scientific Notation Chapter 4 Section 3

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 Examples of numbers in scientific notation 6000 = 6 x 103 6,160,000,000 = 6.16 x 109 0.0000001 = 1.0 x 10-7

To Write a Number in 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: 3.201 x 1010 3.201 x 10,000,000,000 Move 10 places to the right 32,010,000,000 Example: 5.23 x 10-2 5.23 x 1/100 Move 2 place to the left 0.0523

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 1/1000 1 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 left 0.076 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 right 472,100 meters Write 12.5 nanometers without the metric prefix. 12.5 x 10-9 move three places to the left 0.0000000125 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 right 84,000

Calculation using Scientific Notation Example: Divide and write in Scientific Notation.

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 kg How much greater is the weight of the Earth than the weight of its Moon? How many times greater is the weight of the Earth than the weight of its moon? 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