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Do NOW. Express 6,020,000,000,000 in scientific notation Express 0.0000305 in scientific notation. Scientific Notation. September 13, 2011. Objective. SWBAT correctly convert from standard numbers into scientific notation, and back on an exit slip. What is Scientific Notation?.

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  1. Do NOW Express 6,020,000,000,000 in scientific notation Express 0.0000305 in scientific notation

  2. Scientific Notation September 13, 2011

  3. Objective • SWBAT correctly convert from standard numbers into scientific notation, and back on an exit slip.

  4. What is Scientific Notation? • Scientific Notation is used to express very large and very small numbers more easily. • It is a way of writing a number with “Powers of Ten” • If number is greater than 1 : the Power of Ten is POSITIVE. • If number is smaller than 1: the Power of Ten is NEGATIVE.

  5. Statistics: Hope Diamond • Made of the element Carbon • Weight: 45 carats • Weight: 9000 mg = 9 g • Mass of one Carbon atom: 2X10-23 g • 4.6X1023 atoms • LOTS OF ZEROS! TOO MUCH TO WRITE.

  6. RULES 1.23 x 104 EXPONENT:Positive for big numbers, Negative for fractions! BASE:Always 10! NUMBER: Decimal always after first digit

  7. Conversion: Greater than 1 Greater than 1 Example Hillary Clinton makes: Standard Notation: $186,600.00 per year Step 1: 1.86600.00 Step 2: Count 5 numbers to decimal Step 3: coefficient is 5 Answer: 1.86 x 10 5 • Write a decimal after the first digit on the left • Count how many numbers are still after decimal and stop at original decimal point • Write the coefficient * 10 POSITIVE exp

  8. Conversion: Less than 1 Less than 1 Example A germ is: .00000179 centimeters long, convert to Sci Not. Step 1: 1.79 Step 2: moved 6 digits to the right Step 3: the exponent will be -6 (we moved to the right) Answer 1.79 x 10 -6 • Look where the decimal already is • Move the decimal to the rightof the first non-zero digit • Count how many digits you moved • Write this as your base 10 NEGATIVEexp

  9. Guided Practice • Chris Paul has 4,984 career assists. Write this in scientific notation • 4.984 x 103 assists • Will Smith makes $35,000,000 per film. Write this in scientific notation. • $3.5 x 107

  10. Backwards: Greater than 1 Steps to go Backwards >1 Example Convert: 4.82 X 10 5 Move 5 to the right 482,000 • Move the decimal same number of spaces to the right as the positive exponent

  11. Backwards: Less than 1 To go Backwards Less than 1 Example Convert: 1.75 X 10 -6 Move 6 to the left .00000175 • Move the decimal same number of spaces to the left as the positive exponent

  12. Guided Practice Reverse • Oprah makes 2.23 x 10 8 dollars/year. Write this in standard notation. • $ 223,000,000 • A human hair is 56 x 10 -6 meters thick. Write this in standard notation. • .0000056 meters

  13. Independent • On your own, worksheet!

  14. WRITING # IN SCI NOTATION

  15. WRITING SCI NOTATION AS # (Standard)

  16. Exit Slip • Write out the following numbers in scientific notation: • .75 • 0.0000000033939 • Write out the following number in standard notation: • 7.39 * 108

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