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Scientific Notation and SI Prefixes Handling the Big and the Small

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Powers of Ten In science we use powers of ten to handle the vast range of scale in the universe Many physical quantities can be very large or very small

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Power Math ExponentPower of Ten ValueName -910 -9 0.000000001One Billionth -610 -6 0.000001One Millionth -310 -3 0.001One Thousandth -210 -2 0.01One Hundredth 10 -1 0.1One Tenth 010 0 1One 110 1 10Ten 210 2 100Hundred 310 3 1000Thousand 610 6 1,000,000Million 910 9 1,000,000,000Billion

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Scientific Notation Scientific notation is the standard method of handling large and small numbers – SN can handle any number, not just big and small – SN exists for our convenience – SN is neither better nor worse than other forms – We use SN at our discretion for purposes of clarity and ease of use – When numbers are expressed in SN, the number of significant figures is explicit and can no longer be ambiguous

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Standard Form The standard form of SN is most often used The standard form is just a convention to aid communication (you don’t have to always use it) 1.23 × 10 11 1 coefficient 10 base = 10 exponent = any integer Examples: 103,000 = 1.03 × 10 5 0.00022 = 2.2 × 10 4 coefficientbase exponent

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Scientific Notation and Calculators Scientific calculators have a SN function that makes our lives much easier! Use it! The button usually says either “EE” or “Exp” To put in 1.23 × 10 11 you type “1.23” then “EE” then “11” and it will show “1.23E+11” It will give answers in the same form: “5.76E-6” means “5.76 × 10 6 ” Once you have entered a SN value in this way, the calculator treats it as one inseparable number

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SI Prefixes Another way to handle big and small quantities is with SI prefixes SI prefixes modify units by powers of ten For example kilo- (k) can be added to a unit to make the unit larger by a factor of 1000 One kilometer (km) equals a thousand meters In other words, “k” has a value of 1000 or 10 3 1 km = 1000 m = 10 3 m To convert km to m just substitute 10 3 for k Example: 5.2 km = 5.2(10 3 )m = 5.2 10 3 m

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SI Prefixes (cont.) We can use kilo- with any unit to create units a thousand times bigger: – second (s) kilosecond (ks) – gram (g) kilogram (kg) – newton (N) kilonewton (kN) Other prefixes like centi- (c) and milli- (m) make units smaller: 1 cm = (1/100) m = 10 -2 m 1 mm = (1/1000) m = 10 -3 m

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The Full Set of Prefixes

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SI Prefixes and scientific notation work well together to offer us more choices for clarity – Examples: 5.1 × 10 3 m = 5.1 mm 9.38 × 10 5 m = 9.38 × 10 2 km = 938 km 13700 g = 1.37 × 10 4 g = 13.7 kg mill-meterkilo-meterkilo-gram SI Prefixes and Sci. Not.

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Common Prefixes Of the 20 prefixes, only about half of them are commonly used in science and industry Here are the prefixes you should memorize: PowerPrefixAbbreviation 10 9 nano-n 10 6 micro- 10 3 milli-m 10 2 centi-c 10 3 kilo-k 10 6 mega-M 10 9 giga-G

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Summary Scientific notation uses powers of ten to express large and small numbers more succinctly Calculators help us use scientific notation SI Prefixes allow us to create new units that are powers of ten bigger or smaller Scientific notation and unit prefixes together give us a lot of choices and flexibility We should memorize and use the most common prefixes because they are part of the scientific language

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