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Scientific Notation

Scientific Notation. Often used to express very large or very small numbers. Also used to maintain correct number of significant figures. Form: (# from 1 to 9.999) x 10 exponent 800 = 8 x 10 x 10 = 8 x 10 2 2531 = 2.531 x 10 x 10 x 10

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Scientific Notation

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  1. Scientific Notation Often used to express very large or very small numbers. Also used to maintain correct number of significant figures.

  2. Form: (# from 1 to 9.999) x 10exponent 800 = 8 x 10 x 10 = 8 x 102 2531 = 2.531 x 10 x 10 x 10 = 2.531 x 103 0.0014 = 1.4 / 10 / 10 / 10 = 1.4 x 10-3

  3. 000000187000000 . . Change to standard form. 1.87 x 10–5 = 3.7 x 108 = 7.88 x 101 = 2.164 x 10–2 = 0.0000187 370,000,000 78.8 0.02164

  4. Change to scientific notation. 12,340 = 0.369 = 0.008 = 1,000,000,000 = 1.234 x 104 3.69 x 10–1 8 x 10–3 1 x 109

  5. EE EXP Using the Exponent Keyon a Calculator

  6. 6 6 6 6 6 1 1 0 0 0 0 0 0 0 x x y x EE EE EE y x 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 . . . . . How to type out 6.02 x 1023: How to type out 6.02 x 1023: EE or EXP means “times 10 to the…” Don’t do it like this… WRONG! WRONG! …or like this… …or like this: TOO MUCH WORK.

  7. Also, know when to hit your (–) sign… …before the number, …after the number, …or either one.

  8. Type this calculation in like this: 1.2 x 105 2.8 x 1013 1 2 Calculator gives… 4.2857143 –09 1 8 3 2 5 or… 4.2857143 E–09 EE EE This is NOT written… 4.3–9 4.3 x 10–9 . . or 4.3 E –9 = Example: But instead is written…

  9. = -6.525 x 10-9 report -6.5 x 10-9 (2 sig. figs.) = 5.3505 x 103 or 5350.5 report 5.35 x 103 (3 sig. figs.) = 5.84178499 x 10-13 report 5.84 x 10-13 (3 sig. figs.) = 2.904 x 1023 report 2.9 x 1023 (2 sig. figs.) = -3.07122 x 1016 report -3.1 x 1016 (2 sig. figs.)

  10. Scientific Notation • Scientific Notation • Converting Numbers to Scientific Notation • How to Use a Scientific Calculator

  11. Scientific Notation We often use very small and very large numbers in chemistry. Scientific notation is a method to express these numbers in a manageable fashion. Thus 0.000 000 1 cm can be written 1 x 10-7 cm. Lets see why… Scientific notation expresses a number as the product of two factors, the first falling between 1 and 10 and the second being a power of 10.

  12. Method to express really big or small numbers. Format is Mantissa x Base Power Decimal part of original number Decimal you moved 6.02 x 1023 We just move the decimal point around. 602000000000000000000000

  13. Scientific Notation 5000 = 5x103 or 5 3 5x (10x10x10) 5x1000 5000 Numbers > one have a positive exponent. Numbers < one have a negative exponent. Numbers are written in the form M x10n, where the factor M is a number greater than or equal to 1 but less than 10 and n is a whole number. EE x10n

  14. Converting Numbers to Scientific Notation 2.205 x 10-5 0 . 0 0 0 0 2 2 0 5 1 2 3 4 5 In scientific notation, a number is separated into two parts. The first part is a number between 1 and 10. The second part is a power of ten.

  15. . Divide: (5.44 x 107) (8.1 x 104) . How to Use a Scientific Calculator 671.604938 5.44 8.1 54400000. 04 00 07 00 How to enter this on a calculator: . . 5.44 7 8.1 4 EE EE ENTER OR . . 5.44 7 8.1 4 EXP = EXP 671.6049383 rounded to 6.7 x 102 Davis, Metcalfe, Williams, Castka, Modern Chemistry, 1999, page 52

  16. Rule for MultiplicationCalculating with Numbers Written in Scientific Notation When multiplying numbers in scientific notation, multiply the first factors andadd the exponents. Sample Problem: Multiply 3.2 x 10-7 by 2.1 x 105 (3.2) x (2.1) = 6.72 6.72 x 10-2 (-7) + (5) = -2 or 10-2 Exercise: Multiply 14.6 x 107 by 1.5 x 104 2.19 x 1012

  17. Rule for DivisionCalculating with Numbers Written in Scientific Notation When dividing numbers in scientific notation, divide the first factorin the numerator by the first factor in the denominator. Then subtract the exponent in the denominator from the exponent in the numerator. Sample Problem: Divide 6.4 x 106 by 1.7 x 102 . (6.4) (1.7) = 3.76 . 3.76 x 104 (6) - (2) = 4 or 104 Exercise: Divide 2.4 x 10-7 by 3.1 x 1014 7.74 x 10-22

  18. Rule for Addition and SubtractionCalculating with Numbers Written in Scientific Notation In order to add or subtract numbers written in scientific notation, you must express them with thesame power of 10. Sample Problem: Add 5.8 x 103 and 2.16 x 104 2.74 x 104 (5.8 x103) + (21.6 x103) = 27.4 x 103 Exercise: Add 8.32 x 10-7 and 1.2 x 10-5 1.28 x 10-5

  19. Using Scientific Notation for Expressing the Correct Number of Significant Figures Measurement Number of significant figures it contains Measurement Number of significant figures it contains 2 2 7 1 5 4 4 25 g 0.030 kg 1.240560 x 106 mg 6 x 104 sec 246.31 g 20.06 cm 1.050 m 0.12 kg 1240560. cm 6000000 kg 6.00 x 106 kg 409 cm 29.200 cm 0.02500 g 2 7 1 3 3 5 4

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