1. Measuring

2. What are Significant Figures Any digit of a number that is known with certainty. They tell you how precise a measurement is. Any digit of a number that is known with certainty. They tell you how precise a measurement is. Recording Sig Figs Recording Sig Figs  Sig figs in a measurement include the known digits plus a final estimated digit. 2.35 cm

3. Significant Figure Rules  Count all numbers EXCEPT:  Leading zeros -- 0.0025 *Decimal present start from left until you get your first non zero number  Trailing zeros without a decimal point -- 2,500 *Decimal absent start from right until you get your first non zero number

4. 4. 0.080 3. 5,280 2. 402 1. 23.50 C. Significant Figures Counting Sig Fig Examples 1. 23.50 2. 402 3. 5,280 4. 0.080 4 sig figs 3 sig figs 2 sig figs

5. Applying your rules 520.36 ? sig figs 520.36 ? sig figs 1.00250? sig figs 1.00250? sig figs 60? sig figs 60? sig figs 458200000? sig figs 458200000? sig figs 0.250000? sig figs 0.250000? sig figs 0.0063000? sig figs 0.0063000? sig figs

6. Applying your rules 520.36 5 sig figs 520.36 5 sig figs 1.002506 sig figs 1.002506 sig figs 601 sig figs 601 sig figs 4582000004 sig figs 4582000004 sig figs 0.2500006 sig figs 0.2500006 sig figs 0.00630005 sig figs 0.00630005 sig figs

7. Significant Figure Rules cont. Calculating with Sig Figs Calculating with Sig Figs  Multiply/Divide - The # with the fewest sig figs determines the # of sig figs in the answer. (13.91g/cm 3 ) * (23.3cm 3 ) = 324.103g 324 g 4 SF3 SF

8. Significant Figure Rules cont. Calculating with Sig Figs (con’t) Calculating with Sig Figs (con’t)  Add/Subtract – same # of digits to the rights of the decimal as the measurement with the smallest # of digits to the right of the decimal. 3.75 mL + 4.1 mL 7.85 mL  7.9 mL 3.75 mL + 4.1 mL 7.85 mL

9. Significant Figure Rules cont.  Exact Numbers do not limit the # of sig figs in the answer.  Counting numbers: 12 students  Exact conversions: 1 m = 100 cm  “1” in any conversion: 1 in = 2.54 cm

10. 1. (15.30 g) ÷ (6.4 mL) = 2.390625 g/mL  18.1 g 2. 18.9g - 0.84 g 18.06 g 4 SF2 SF  2.4 g/mL 2 SF Practice Problems

11. Rounding! RULE 1. If the first digit you remove is 4 or less, drop it and all following digits. RULE 2. If the first digit removed is 5 or greater, round up by adding 1 to the last digit kept. If a calculation has several steps, it is best to round off at the end.

12. Examples Make the following into a 3 Sig Fig number 1.1.5587 2..0037421 3.1367 4.128,522 5.1.6683  10 6 1.56.00374 1370 129,000 1.67  10 6 Your Final number must be of the same value as the number you started with, 129,000 and not 129

13. Examples of Rounding For example you want a 4 Sig Fig number 4965.03 780,582 1999.5 0 is dropped, it is <5 8 is dropped, it is >5; Note you must include the 0’s 5 is dropped it is = 5; note you need a 4 Sig Fig 4965 780,600 2000.

14. Scientific Notation Converting into Sci. Notation: Converting into Sci. Notation:  Move decimal until there’s 1 digit to its left. (1-9) Places moved = exponent. 65,000 kg  6.5 × 10 4 kg Only include sig figs.

15. Scientific Notation Rules Large # (>1)  positive exponent Large # (>1)  positive exponent (move to the left) (move to the left) Small # (<1)  negative exponent Small # (<1)  negative exponent (move to the right) To work backwards from scientific notation to decimal notation just do the opposite. To work backwards from scientific notation to decimal notation just do the opposite.

16. Scientific Notation 1. 2,400,000  g 2. 0.00256 kg 3.7  10 -5 km 4.6.2  10 4 mm Practice Problems 2.4  10 6  g 2.56  10 -3 kg 0.00007 km 62,000 mm

17. Scientific Notation Calculating with Sci. Notation Calculating with Sci. Notation (5.44 × 10 7 g) ÷ (8.1 × 10 4 mol) = 5.44 EXP EE ÷ ÷ EXP EE ENTER EXE 78.1 4 = 671.6049383= 670 g/mol= 6.7 × 10 2 g/mol Type on your calculator:

18. SI Prefix Conversions 1.Find the difference between the exponents of the two prefixes. 2.Move the decimal that many places. 3.Be sure to maintain sig figs! To the left or right?

19. Copyright © 2010 Ryan P. Murphy

21. “I love my chocolate Milk!” Copyright © 2010 Ryan P. Murphy

23. “Oh no!”

24. Copyright © 2010 Ryan P. Murphy

31. King - Kilometer1000m10 3 King - Kilometer1000m10 3 Henry- Hectometer100m10 2 Henry- Hectometer100m10 2 Died - Decameter10m10 1 Died - Decameter10m10 1 By - Base Unit1m10 0 By - Base Unit1m10 0 Drinking - Decimeter.1m 10 -1 Drinking - Decimeter.1m 10 -1 Chocolate - Centimeter.01m10 -2 Chocolate - Centimeter.01m10 -2 Milk - Millimeter.001m10 -3 Milk - Millimeter.001m10 -3 Copyright © 2010 Ryan P. Murphy

32. SI Prefix Conversions 1) 20 cm = ______________ m 2) 0.032 L = ______________ mL 3) 45  m = ______________ nm 4) 805 dm = ______________ km 0.2 0.0805 45,000 32

33. Dimensional Analysis The “Factor-Label” Method The “Factor-Label” Method  Units, or “labels” are canceled, or “factored” out

34. Dimensional Analysis Steps: Steps: 1. Identify starting & ending units. 2. Line up conversion factors so units cancel. 3. Multiply all top numbers & divide by each bottom number. 4. Check units & answer.

35. Dimensional Analysis 1. Taft football needs 550 cm for a 1st down. How many yards is this? 550 cm 1 in 2.54 cm = 6.0 yd cmyd 1 ft 12 in 1 yd 3 ft 1 in = 2.54 cm 1 ft = 12 in 1 yd = 3 ft