1. Unit 1 – Lecture 5

2. 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.

3. 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

4. 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 * 10 15 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

5. Change into Scientific Notation 10,000 moving the decimal 4 places to the left = 1 * 10 4.000 000 000 000 004 moving decimal 15x to the right =4 * 10 -15 12,357 moving decimal 4x to the left = 1.2357 x 10 4.003 675 78 moving decimal 3x to the right = 3.67578 x 10 -3 200.0 * 10 2 moving decimal 2x to the left = 2.000 * 10 4

6. Check Your Warm-Ups 3427 cm = 3.427 x 10 3 cm 0.502 km = 5.02 x 10 -1 km 34.378 ml = 3.4378 x 10 1 ml.0078 x 10 4 seconds = 78 OR 7.8 x 10 1

7. Check Your Warm-Ups 1 x 10 3 cm = 1,000 cm 2.45 x 10 4 cm = 24,500 cm 3.787 x 10 2 km = 378.7 km 7.0076 x 10 5 L = 700,760 L

8. Significant Figures used to express the certainty of a measured value ex: 2, 2.0, 2.00 2 = 1-3 [+/- 1] 2.0 = 1.9-2.1 [+/- 0.1] 2.00 = 1.99-2.01 [+/-.01]

9. 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

10. 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

11. 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 210000 both have two significant figures, while 210. has three and 210.00 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

12. 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 10 28 has five significant figures

13. Sig Fig Practice Count the # of Sig Figs 1.05 g three [1.05 * 10 0 ] 0.0003040 mm four [3.040 * 10 -4 ] 29000 two [2.9 * 10 4 ] 29000. five [2.9000 * 10 4 ] 0.90 * 10 45 L two [9.0 * 10 44 ]

14. Sig Fig Practice Round each to 3 Sig Figs: [find the third sig fig, then round to that number] 77.0653 77.1 [7.71 * 10 1 ] 6,300,178.2 6.30 * 10 6 0.00023350.000234 [2.34 * 10 -4 ]

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