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Scientific Notation Mrs. Laubach

Scientific Notation Mrs. Laubach. Scientific Notation. A way of writing very large or very small numbers of the form c • 10 n where c is a number 1 ≤ c < 10 and n is an integer

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Scientific Notation Mrs. Laubach

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  1. Scientific Notation Mrs. Laubach

  2. Scientific Notation • A way of writing very large or very small numbers of the form c • 10n where c is a number 1 ≤ c < 10 and n is an integer • The number 123,000,000,000 (standard form or standard notation of the number) in scientific notation is written as: 1.23 x 1011 • The first number 1.23 is called the coefficient. It must be greater than or equal to 1 and less than 10—only one non-zero digit in front of the decimal point • The second number is called the base. It must always be 10 in scientific notation. The base number 10 is always written in exponent form. In the number 1.23 x 1011 the number 11 is referred to as the exponent or power of ten.

  3. Standard Form to Scientific Notation • Given:  4,750,000 4.75 (moved decimal point 6 decimal places left) Answer:  4.75 X 106 The original number was greater than 1 so the exponent is positive • Given:  0.000789 7.89 (moved decimal point 4 decimal places right) Answer:  7.89 x 10-4 The original number was less than 1 so the exponent is negative

  4. Scientific Notation to Standard Form • Given:  1.015 x 10-8 0.00000001015 (moved decimal 8 places left—negative direction on a number line)—Answer:  0.00000001015 Negative exponent moves decimal to the left • Given:  5.024 x 103 5,024  (move decimal 3 places right—positive direction on a number line)—Answer:  5,024   Positive exponent moves decimal to the right

  5. More Scientific Notation Info. • The base 10 to a positive exponent means that the coefficient is getting larger e.g. 5.6 • 105 = 560,000 • The base 10 to a negative exponent means that the coefficient will get smaller e.g. 5.6 • 10-5 = .000056; remember, 10-5 really means (1/105)

  6. Multiplying and Dividing numbers in Scientific Notation • One of the advantages of scientific notation is its ease of use when performing computations.

  7. To Multiply #’s in Scientific Notation To multiply two numbers expressed in scientific notation, simply multiply the numbers out front and add the exponents of the base 10.Generically speaking, this process is expressed as: (using the commutative and associative properties of multiplication) (n  10a) • (m  10b) = (n  m)  10a+b

  8. Example 1--Multiplying (3 x 105) • (2 x 102) = (3 x 2) • (105 x 102) = 6 x 107 

  9. Example 2--Multiplying (5.1 x 104) • (2.5 x 103) = 12.75 x 107  • Be careful—This new answer is no longer in proper scientific notation. (12.75 in correct SN is (1.275 x 101) x 107 = 1.275 x 108) • Proper scientific notation is 1.275 x 108

  10. To Divide #’s in Scientific Notation To divide two numbers expressed in scientific notation, simply divide the numbers out front and subtract the exponents.Generically speaking, this process is expressed as:

  11. Example2 & 3--Dividing

  12. Complete this table. Number in Standard Form Move the decimal to the left or right to make the number greater than or equal to 1, but less than 10. Count the number of places you moved the decimal. Did you move it to the left or right? Number in Scientific Notation 217,000 2.1 7 0 0 0 . 5 places to the left 2.17 × 105 0.00095 0 . 0 0 0 9 . 5 4 places to the right 2.17 × 10–4 0.0000184 99,000,000

  13. Complete this table. Number in Standard Form Move the decimal to the left or right to make the number greater than or equal to 1, but less than 10. Count the number of places you moved the decimal. Did you move it to the left or right? Number in Scientific Notation 217,000 2.1 7 0 0 0 . 5 places to the left 2.17 × 105 0.00095 0 . 0 0 0 9 . 5 4 places to the right 2.17 × 10–4 places to the 5 right 0.0000184 0 . 0 0 0 0 1 . 8 4 1.84 × 10–5 places to the 7 left 99,000,000 9 . 9 0 0 0 0 0 0 . 9.9 × 107

  14. Facts About Earth, Saturn, and the Speed of Light Light travels at a rate of about 186,000 miles per second! APPROXIMATE PLANET DISTANCE FROM SUN (in miles) Saturn 887,200,000 Earth 93,000,000

  15. Some Practice Rewrite in scientific notation: • a. 0.011205 • b. 140,000,000 • c. 0.00000067 • d. 30,720,000,000 Rewrite in decimal (standard) form (notations): • a. 4.82 x 103 • b. 5 x 109 • c. 7.04 x 10−6 • d. 1.112 x 10−2

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