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# Metric conversions, significant digits, exponent shortcuts, percent yield, dimensional analysis

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Metric conversions, significant digits, exponent shortcuts, percent yield, dimensional analysis for high school students

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### Metric conversions, significant digits, exponent shortcuts, percent yield, dimensional analysis

1. 1. Metric conversions, significant digits, exponent shortcuts, percent yield, dimensional analysis.
2. 2.    Volume: How much space something takes up, measured in Liters or milliliters (cm3). Mass(weight): measured in grams, milligrams or kilograms. Length: measured in meters, millimeters, or centimeters.
3. 3.        Kilo-K Hecta-H Deka-Dk Base units= meters, Liters, grams Deci-d Centi-c Milli-m
4. 4. km Hm dkm m dm cm mm 25. 2500. To change metric units, simply slide the decimal place along the scale from one unit to another. 25 meters becomes 2500 centimeters.
5. 5. Find D for: A piece of cork that displaces 2 ml water weighs .41 grams. (.205 g/ml) A rock that displaces 10 ml water has a weight of 30 grams. (3 g/ml) A chunk of ice which has a volume of 25 ml weighs 23 grams. (.91 g/ml)
6. 6. The great advantage of using metric units is that they are in multiples of ten. This means that you can simply move decimal points to go from one unit to another!
7. 7.       23.5 g to mg (23,500 mg) 435.7 ml to L (.4357 L) .223 km to m (223m) 22.57 cm to m (.2257 cm) 450.3 L to ml 45 mg to g
8. 8.       Significant Digits – the number of certain and estimated digits in a number. Zeroes to left of decimal point and to left of an integer do not count as significant. All other zeroes do count as significant. 31.76 (4 s.d.)is more accurate than 31.7 (3 s.d.) .009210 (4 s.d.) = 9.210 x 10-3 .0090210 (5 s.d.) = 9.0210 x 10-3
9. 9. When doing math, your answer can only have as many sigdigs as the lesser number of sigdigs: 1.12 + 2.243 = 3.363 = 3.36 (3 sigdigs) (4 sigdigs) (4 sigdigs) (3 sigdigs) This answer can only have 3 significant digits since 1.12 only has 3 digdigs.
10. 10.    The exponents you will use in this class represent numbers which have the number of decimal places in the exponent 100 = 1; 101 = 10; 102 = 100 and so on. Positive exponents push the decimal place to the right: 2.35 x 103 is 2,350 Negative exponents push the decimal place to the left: 2.35 x 10-3 is .00235
11. 11. When multiplying exponential numbers, multiply the first two, then add the exponents: 1.2 x 103 x 1.2 x 103 = 1.44 x 106  When dividing exponential numbers, divide the first two, then subtract the exponents: 1.2 x 103 / 1.2 x 103 = 1.0 x 100 =1 
12. 12.  To add exponents, move the decimal place to get the same exponents, then add the numbers, keeping the exponent. 1 x 102 + 1 x 103 = 1 x 102 + 10 x 102 = 11 x 102  To subtract exponents, move the decimal place to get the same exponents, then subtract the numbers, keeping the exponent. 1 x 103 - 1 x 102 = 10 x 102 - 1 x 102 = 9 x 102
13. 13.     5.4 x 107 + 2.7 x 106 = 16 15 2.3 x 10 – 1.8 x 10 = 24 22 8.4 x 10 / 4.2 x 10 = 3.2 x 103 x 2 x 1012 =
14. 14.   Percent Yield = Actual x 100 Expected Percent Error = Actual – Expected x 100 Expected
15. 15.  Used to convert units. Multiply the given by the unit you want to find on the top, and the unit you want to cancel on the bottom.  10.5 mm = ? Meters 10.5 mm x 1 meter = .0105 meters 1,000 mm 