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 always ONE number before the decimal.

Scientific Notation – cont’d A * 10 B 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 * 10 0 move decimal zero times 1 with zero zeros behind it; = 1 1* 10 5 move the decimal 5x to the right 1 with 5 zeros behind it; = 100,000 5 * move the decimal 15x to the right 5 with 15 zeros after it; = * move decimal 2x to the LEFT =.01

Change into Scientific Notation 10,000 moving the decimal 4 places to the left = 1 * moving decimal 15x to the right =4 * ,357 moving decimal 4x to the left = x moving decimal 3x to the right = x * 10 2 moving decimal 2x to the left = * 10 4

Check Your Warm-Ups 3427 cm = x 10 3 cm km = 5.02 x km ml = x 10 1 ml.0078 x 10 4 seconds = 78 OR 7.8 x 10 1

Check Your Warm-Ups 1 x 10 3 cm = 1,000 cm 2.45 x 10 4 cm = 24,500 cm x 10 2 km = km x 10 5 L = 700,760 L

Significant Figures used to express the certainty of a measured value ex: 2, 2.0, = 1-3 [+/- 1] 2.0 = [+/- 0.1] 2.00 = [+/-.01]

Significant Figures – 5 rules Always count nonzero digits Example: 21 has two significant figures, while has four Never count leading zeros [zeros to the left of the first non-zero digit] Example: 021 and 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; has six

Sig Fig Rules – cont’d Count trailing zeros if and only if the # contains a decimal point [even if there is nothing after it] Example: 210 and both have two significant figures, while 210. has three and has five the difference is in how accurately they were measured… 210 is accurate to only the “tens” place 210. is accurate to the “ones” place

Sig Fig Rules – cont’d For numbers expressed in scientific notation, ignore the exponent and apply Rules 1-4 to the coefficient Example: x has five significant figures

Sig Fig Practice Count the # of Sig Figs 1.05 g three [1.05 * 10 0 ] mm four [3.040 * ] two [2.9 * 10 4 ] five [ * 10 4 ] 0.90 * L two [9.0 * ]

Sig Fig Practice Round each to 3 Sig Figs: [find the third sig fig, then round to that number] [7.71 * 10 1 ] 6,300, * [2.34 * ]

Homework Complete: Scientific Notation w/s [pgs 20-21] Sig Figs w/s [pgs 22] GO TO 3301 TOMORROW!!!