Scientific Notation and SI Prefixes Handling the Big and the Small 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 Power Math Exponent Power of Ten -9 10-9 -6 10-6 Value Name 0.000000001 0.000001 One Billionth One Millionth -3 10-3 0.001 One Thousandth -2 10-2 0.01 One Hundredth -1 10-1 0.1 One Tenth 0 100 1 One 1 101 10 Ten 2 102 100 Hundred 3 103 1000 Thousand 6 106 1,000,000 Million 9 109 1,000,000,000 Billion 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 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 × 1011 coefficient base exponent 1 coefficient 10 base = 10 exponent = any integer • Examples: 103,000 = 1.03 × 105 0.00022 = 2.2 × 104 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 × 1011 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 × 106” • Once you have entered a SN value in this way, the calculator treats it as one inseparable number 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 103 1 km = 1000 m = 103 m • To convert km to m just substitute 103 for k Example: 5.2 km = 5.2(103)m = 5.2 103 m 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 The Full Set of Prefixes SI Prefixes and Sci. Not. • SI Prefixes and scientific notation work well together to offer us more choices for clarity – Examples: 5.1 × 103 m = 5.1 mm mill- meter 9.38 × 105 m = 9.38 × 102 km = 938 km kilo- meter 13700 g = 1.37 × 104 g = 13.7 kg kilo- gram 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: Power 109 106 103 102 103 106 109 Prefix nanomicromillicentikilomegagiga- Abbreviation n m c k M G 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