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SCIENTIFIC NOTATION

SCIENTIFIC NOTATION. An Introduction. SCIENTIFIC NOTATION. Scientific notation is used to express very large or very small numbers. A number in scientific notation is written as the product of a number (integer or decimal) and a power of 10.

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SCIENTIFIC NOTATION

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  1. SCIENTIFIC NOTATION An Introduction

  2. SCIENTIFIC NOTATION Scientific notation is used to express very large or very small numbers. A number in scientific notation is written as the product of a number (integer or decimal) and a power of 10. The number has one digit to the left of the decimal point. The power of ten indicates how many places the decimal point was moved. .

  3. EXAMPLES • 5 500 000 • = 5.5 x 106 We moved the decimal 6 places to the left. A number between 1 and 10

  4. EXAMPLE #2 Numbers less than 1 will have a negative exponent. • 0.0075 • = 7.5 x 10-3 We moved the decimal 3 places to the right. A number between 1 and 10

  5. EXAMPLE #3 • CHANGE SCIENTIFIC NOTATION TO STANDARD FORM 2.35 x 108 = 2.35 x 100 000 000 = 235 000 000 Standard form Move the decimal 8 places to the right

  6. EXAMPLE #4 9 x 10-5 = 9 x 0.000 01 = 0.000 09 Standard form Move the decimal 5 places to the left

  7. TRY THESE • Express in scientific notation • 1) 421.96 • 2) 0.0421 • 3) 0.000 56 • 4) 467 000 000

  8. TRY THESE • Change to Standard Form • 1) 4.21 x 105 • 2) 0.06 x 103 • 3) 5.73 x 10-4 • 4) 4.321 x 10-5

  9. Multiplication and Scientific Notation • To multiply (3.1 x 104)(2 x105) • use the commutative property • the associative property (grouping of multiplication doesn’t matter) to get • Then use the exponent rules to get the final result

  10. Multiplication and Scientific Notation • To multiply (3.1 x 104)(2 x105) • 6.2 x 109

  11. Examples (3x108)(1.5x102)

  12. (3x108)(1.5x102) =4.5x1031

  13. Examples (2.1x104) (4x10-12)

  14. Examples (2.1x104) (4x10-12) =8.4x10-8

  15. Examples Note the answer we got=26.68x1014 Notice: What is wrong with this answer? Although the answer is correct, the number is not in scientific notation. To finish the problem, move the decimal one space left and increase the exponent by one. 26.68x1014 = 2.668x1015

  16. Divisionand Scientific Notation Division works in a similar way.

  17. Divisionand Scientific Notation Division works in a similar way.

  18. Divisionand Scientific Notation Division works in a similar way.

  19. Divisionand Scientific Notation Division works in a similar way.

  20. Divisionand Scientific Notation Division works in a similar way.

  21. Divisionand Scientific Notation Division works in a similar way.

  22. Calculator notation • Some calculators show scientific notation the same way we have written them here. • Some use EE. They write 3.456 EE5 to mean 3.456 x105. • Some write the same thing with this in the screen 3.4560505. There are several ways electronic equipment displays scientific notation. Look in your user’s manual to see how it is displayed on your calculator.

  23. Multiplication and Division with Scientific Notation http://www.algebralab.org/practice/practice.aspx?file=Algebra_MultiplyingDividingScientificNotationNumbers.xml • Scientific Notation Practice http://staff.argyll.epsb.ca/jreed/math7/strand1/1103.htm Conversion from standard to scientific notation Calculator practice Word search • Practice Scientific Notation Quiz http://library.thinkquest.org/20991/textonly/quizzes/alg/q11/test.html

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