Fundamentals of Physics I Scientific notation and the metric system

Scientific Notation Working with very big and very small numbers A whole number and a decimal multiplied by a power of 10 Examples: 6.5 x 109 3.4 x 1010 8 x 10-3

Converting to scientific notation Move the decimal 5,400,000.0 5.4 x 106 0.00000000345 3.45 x 10-9 HINT: Large numbers  positive exponents Small numbers  negative exponents

Converting to decimal form Positive exponent— move decimal to the right Negative exponent—move the decimal to left 4.5 x 107 45,000,000.0 7.89 x 10-4 0.000789 10-2 Think of this as 1 x 10-2 0.01 What about 100? 100 = 1 So 3.5 would be 3.5 x 100

Metric System Prefix/Multiplier Symbol 10n Multiplier Giga- G 109 1,000,000,000 Mega- M 106 1,000,000 Kilo- k 103 1,000 Hecto- h 102 100 Deka- da 101 10 Base- meter, liter, gram 1 Deci- d 10-1 0.1 Centi- c 10-2 0.01 Milli- m 10-3 0.001 Micro- μ 10-6 0.000 001 Nano- n 10-9 0.000 000 001

Metric Prefix: Base Units vs. Standard Units Length Meter m Volume Liter m3 Mass Gram kg Base Unit Standard Unit

Try these: ______ cm = 1 meter ______mm = 1 meter 4,000,000 bytes = _______Mbytes 4 Mbytes 85 kilodollars = _______dollars 85,000 dollars

To help you remember try these: 10-2 mental 10-6 scope 106 phone 101 ration

Mini Quiz Convert to Scientific Notation 0.00000456 267,000,000,000 Solve 3. (2.3 x 105) x (4.5 x 10-9) = 4. 26 km = ____ mm 26,000,000 5. 568 µg = ____ g 0.000568 10.35 X 10-4 = 1.035 X 10-3

Conversion Factors Length: 1 in = 2.54 cm 1 mi = 5280 ft 1000 m = 1 km Mass: 1 kg = 2.2 lbs Volume: 354 ml = 12 fl oz. 1 L = 1.06 qts

Examples 2 hrs = ____ min

Examples 3 miles = _____ inches