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Published byBryan Oliver Modified over 2 years ago

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Why is this stuff important?

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

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Form:(# from 1 to 9.999) x 10 exponent 800= 8 x 10 x 10 = 8 x = x 10 x 10 x 10 = x = 1.4 / 10 / 10 / 10 = 1.4 x 10 -3

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Change to standard form x 10 –5 = 3.7 x 10 8 = 7.88 x 10 1 = x 10 –2 = 370,000,

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Change to scientific notation. 12,340 = = = 1,000,000,000 = x x 10 –1 8 x 10 –3 1 x 10 9

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Using the Exponent Key on a Calculator EXPEE 2nd

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EE or EXP means times 10 to the… How to type out 6.02 x : 6EE How to type out 6.02 x : 6EE. 0322

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

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Example: 1.2 x x But instead is written… = 1. 2EE Type this calculation in like this: This is NOT written…4.3 – –09 Calculator gives… E–09 or… 4.3 x 10 –9 4.3 E –9or 2nd

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= x = x 10 3 or = x report -6.5 x (2 sig. figs.) report 5.35 x 10 3 (3 sig. figs.) report 5.84 x (3 sig. figs.) = x report 2.9 x (2 sig. figs.) = x report -3.1 x (2 sig. figs.) (–)

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Rule for Multiplication Calculating with Numbers Written in Scientific Notation When multiplying numbers in scientific notation, multiply the first factors and ADD the exponents. Sample Problem: Multiply (3.2 x )x (2.1 x 10 5) (3.2) x (2.1) = 6.72 (-7) + (5) = -2 or x Exercise: Multiply (14.6 x 10 7 ) X (1.5 x 10 4 ) 2.19 x 10 12

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Rule for Division Calculating with Numbers Written in Scientific Notation When dividing numbers in scientific notation, divide the first factor in 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 10 6 ) by (1.7 x 10 2 ) (6.4) (1.7) = 3.76 (6) - (2) = 4 or x 10 4 Exercise: Divide 2.4 x by 3.1 x x

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Rule for Addition and Subtraction Calculating with Numbers Written in Scientific Notation In order to add or subtract numbers written in scientific notation, you must express them with the same power of 10. Sample Problem: Add (5.8 x 10 3 ) + ( 2.16 x 10 4 ) (5.8 x 10 3 ) + (21.6 x 10 3 ) =27.4 x 10 3 Exercise: Add (8.32 x ) + (1.2 x ) 1.28 x x 10 4

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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 25 g kg x 10 6 mg 6 x 10 4 sec g cm m 0.12 kg cm kg 6.00 x 10 6 kg 409 cm cm g

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