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Scientific Notation & Significant Figures. Unit 1 – Lecture 5. Scientific Notation. Why use scientific notation / powers of 10? hard to use very large or very small numbers Uses Powers of Ten Format = A times 10 B A = coefficient B = number of places decimal moves to express A.
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Scientific Notation & Significant Figures Unit 1 – Lecture 5
Scientific Notation • Why use scientific notation / powers of 10? • hard to use very large or very small numbers • Uses Powers of Ten • Format = • A times 10B • A = coefficient • B = number of places decimal moves to express A
Scientific Notation – cont’d • A * 10B • positive exponent = move decimal to the right • makes the coefficient larger • A * 10-B • negative exponent = move decimal to the left • makes the coefficient smaller
Change out of Scientific Notation • 1 * 100 • move decimal zero times • 1 with zero zeros behind it; = 1 • 1* 105 • move the decimal 5x to the right • 1 with 5 zeros behind it; = 100,000 • 5 * 1015 • move the decimal 15x to the right • 5 with 15 zeros after it; = 5,000,000,000,000,000 • 1 * 10-2 • move decimal 2x to the LEFT • = .01
Change into Scientific Notation • 10,000 • moving the decimal 4 places to the left • = 1 * 104 • .000 000 000 000 004 • moving decimal 15x to the right • =4 * 10-15 • 12,357 • moving decimal 4x to the left • = 1.2357 x 104 • .003 675 78 • moving decimal 3x to the right • = 3.67578 x 10-3 200.0 * 102 moving decimal 2x to the left = 2.000 * 104
Significant Figures – 5 rules • Always count nonzero digits • Example: 21 has two significant figures, while 8.926 has four • Never count leading zeros [zeros to the left of the first non-zero digit] • Example: 021 and 0.021 both have two significant figures
Sig Fig Rules – cont’d • Always count zeros which fall between two nonzero digits • Example: 20.8 has three significant figures; 0.00104009 has six • Count trailing zeros if and only if the # contains a decimal point [even if there is nothing after it] • Example: 210 and 210000 both have two significant figures, while 210. has three and 210.00 has five
Sig Fig Rules – cont’d • For numbers expressed in scientific notation, ignore the exponent and apply Rules 1-4 to the coefficient • Example: -4.2010 x 1028 has five significant figures
Sig Fig Practice Count the # of Sig Figs • 1.05 g • three [1.05 * 100] • 0.0003040 mm • four [3.040 * 10-4] • 29000 • two [2.9 * 104] • 29000. • five [2.9000 * 104] • 0.90 * 1045 L • two [9.0 * 1044] Round each to 3 Sig Figs: • 77.0653 • 77.1 [7.71 * 106] • 6,300,178.2 • 6.30 * 106 • 0.00023350 • .000234 [2.34 * 10-4]
