I. BASIC REVIEW OF METRIC UNITS FUNDAMENTAL UNITS = Meters, Kilograms, Seconds (MKS) CONVERSIONS YOU MUST KNOW BY HEART 1 cm = .01 m 100 cm = 1 m 1km = 1000 m 1 m = .001 km 1 kg = 1000 g 1 g = .001 kg 1 min = 60 s 1 hour = 60 min 1 hour = 3600 s HOW TO CONVERT: A. Rules of Thumb 1. A small # with a big unit = a larger # with a small unit 2. Every time you move the decimal to the right by one place you multiply by 10 3. Every time you move the decimal to the left by one place you divide by 10 FACTOR LABEL METHOD: a shortcut using labeled conversion factors. Conversion factor – a fraction of equivalents with different units for the same property. Exs: 1 hour 1 km 1000 g 3600 s 1000 m 1 kg Conversion factors can be flipped according to what you need. Sample problem: (A) How many seconds are in a 45 minute class period at Eastern Tech? 1. Start with 45 min. Remember that 45 min. has a 1 underneath. 45 min. 1 2. Now, you are converting minutes into seconds, right?! So, you must choose a conversion factor which has those two units. O.K. We know that 60 s = 1 min. Duh! So, we will use one of the following conversion factors to help us: 60 s or 1 min. 1 min. 60 s Now we have to pick the right one to use. Since we are converting TO seconds, we want to get rid of minutes so seconds will be left (on top) in the final answer. So pick the conversion factor labeled with "s" on top. 60 s 1 min. LET IT RIP! OK, lets convert! 45 min. x 60 s = 2700 s 1 1 min. NOW YOU TRY USING THE CONVERSION Name ___________________________________ EQUIVALENTS AT THE TOP OF THE FIRST PAGE. 45 cm = _______ m 8.17 kg = ____________ g 24 hrs. = _____________ s 720 s = _______ h 14 km = ___________ m 83 g = ________kg II. SCIENTIFIC NOTATION Students, numbers are nice. But really BIG numbers or very small numbers can be a pain in the bazoo. So, to avoid writing all those zeroes in such numbers, scientists have come up with a way to use a shorthand expression. It is called scientific notation. As you know, every place in a number is bigger or smaller by 10x. So, scientific notation starts at 1 and uses powers of 10 to replace the zeroes. Ex: 1 x 102 = 100 because there are two zeroes. 1 x 106 = 1 million, because 1,000,000 has six zeroes. 1 x 10-2 = .01 because you start with the no. 1 and go BACK two places. Get it?....(-2).... Always start with the decimal after the ONES place so the final numerical part is a number between 1 and 10. 2,560 = 2.56 x 103 .00099 = 9.9 x 10-4 And 3 = 3 x 100 because the number was already in the ONES place. No moving was necessary. Now, convert these to scientific notation: 6,320,000 = ______________ .000783 = _____________ .000 000 000 000 19 = ________________ How to enter numbers in scientific notation into your calculator. For most calculators, the "E" or "EE" button is used for scientific notation. Casio calculators may use "EXP". The "E" stands for x 10n . For example, look at the following problem: (4.1 x 108)(8.76 x 10-15) = __________________ HERE'S WHAT YOU WOULD PUNCH IN TO SOLVE IT. 4 . 1 E 8 x 8 . 7 6 E –15 = Try these: (9.23 x 109) + (7.6 x 108) = _______________ (6.5 x 106)(3.33 x 10-19) = ________________ (4.67 x 1012) = ________________ (2.2 x 104) – (4.3 x 104) = _________________ (2.40 x 1016)