2 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.
3 Convert Numbers to and from Scientific Notation Examples of numbersin scientific notation6000 = 6 x 1036,160,000,000 = 6.16 x 109= 1.0 x 10-7
4 To Write a Number in Scientific Notation Move the decimal point in the right of the first nonzero digit. ≥1 and <10Count 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
5 Express in Scientific Notation Example: x 10-5Example:1,340,0001.34 x 106
6 Convert a Number from Scientific Notation to Decimal Form Observe the exponent in the power of 10If exponent is positive ≥1 and <10 move the decimal to the right. May have to add zero’sIf 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
7 Express in Decimal Form (without exponents) Example: x 10103.201 x 10,000,000,000Move 10 places to the right32,010,000,000Example: 5.23 x x 1/100 Move 2 place to the left
8 Scientific Notation with a Coefficient of 1 The metric system is used in every westernized nation except the United Stateskilograms, milligrams, gigabytes1 millimeter (m) = 10-3 or 1/10001 megagram (M) = 106 or 1,000,000See other in table on page 253
9 Scientific Notation with a Coefficient of 1 Remember that we assume 1 when no numerical coefficient existsExample:Write 76 millimeter without the metric prefix.76 x move three places to the left0.076 meters
10 Scientific Notation with a Coefficient of 1 Example:Write Kilometers without the metric prefix.472.1 x move three places to the right472,100 metersWrite 12.5 nanometers without the metric prefix.12.5 x move three places to the leftmeters
11 Calculation using Scientific Notation Use the rules of exponentsExample: 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 104Move the decimal place 4 places to the right84,000
12 Calculation using Scientific Notation Example: Divide and write in Scientific Notation.
13 Calculation using Scientific Notation Example: The weight of the Earth is x 1024 kg. The weight of the Earth’s Moon is 7.35 x 1022 kgHow 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.
14 RememberThe numerical value preceding the base must be greater than or equal to 1 but less than 10The sign of the exponent on the base indicates which direction to move the decimal point.Negative moves leftPositive moves right