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Scientific Notation What is it? How do I use it? Why?!?!?! Scientific Notation • Scientific notation, also called power-of-10 notation, is a method of writing extremely large and small numbers. • Scientific notation makes it easy to multiply and divide gigantic and/or very small numbers. • For very large or very small numbers, it is sometimes simpler to use "scientific notation" (so called, because scientists often deal with very large and very small numbers). • The format for writing a number in scientific notation is fairly simple: first digit of the number followed by the decimal point and then all the rest of the digits of the number, times 10 to an appropriate power. Scientific Notation • A number is in Scientific Notation if: – – – – It is in the form of a x 10b a is a decimal. 1< a <10 b is an integer Determine if each of the following is in proper Scientific Notation form. Be prepared to support your answer. Problem: Response: Reason: 1. 3 x 102 2. 0.4 x 102 3. 35 x 102 4. ½ x 102 5. 4.0 x 101/2 6. 3.5 x 10-4 Compare your answers with the table below. Problem: Response: Reason: 1. 3 x 102 YES Follows all rules. 2. 0.4 x 102 NO Decimal part is less than 1. 3. 35 x 102 NO Decimal part is greater than 10. 4. ½ x 102 NO Decimal part is not a decimal and it is less than 1. 5. 4.0 x 101/2 NO Exponent is not an integer. 6. 3.5 x 10-4 YES Follows all rules. To write a number in Scientific Notation: Step 1: • Find the original decimal point, label the decimal point “old”. What if there is not a decimal point? Where is it? .000054 old 43.56 old 4,560,000,000 old To write a number in Scientific Notation: Step 2: • Start on the left and put a new decimal point after the first digit that is NOT a zero. Label this decimal point “new”. Write this number down in front of the x 10. .000054 43.56 4,560,000,000 .00005.4 4.3.56 4.560,000,000 old new 5.4 x 10 new old 4.356 x 10 new 4.6 x 10 old To write a number in Scientific Notation: Step 3: • Count the number of spaces from the new to the old decimal point. This is your exponent. Decimal x 10 Think of a number line, if you count the right, the exponent will be positive, to the left negative. new old old new old new .000054 5…4….3….2……1 1 Counted left, exponent negative. 5.4 x 10 4.3.56 -5 Counted right, exponent positive. 4.356 x 10 1 4.560,000,000 1…..2....3…..4……5..6……7…..8…. Counted right, exponent positive. 4.56 x 10 9 9 To write a number in Scientific Notation: Final Answers .000054 5.4 x 10 5 43.56 4.356 x 10 1 4,560,000,000 4.56 x 10 9 Let’s Practice! • • • • • • • Directions: Label the new and the old decimals. Write in Scientific Notation, OR write the number in standard notation. 5,760,000,000 0.00000765 4.5 x 108 3.8 x 10-5 6,798,000 1.34 x 106 0.000945 • • • • • • • 5.76 x 109 7.65 x 10-6 450,000,000 0.000038 6.798 x 106 1,340,000 9.45 x 10-4