1. CH. 1 - MEASUREMENT I. Units of Measurement

2. Scientific Method

3. A. Derived Units  Combination of base units.  Volume (mL or cm 3 )  Formulas for volume of sphere and cylinder D = mVmV 1 cm 3 = 1 mL 1 dm 3 = 1 L  Density (g/mL or g/cm 3 )  mass per volume

4. B. Density  Density of a substance determines whether that substance will float or sink in a liquid  Density of a substance does not change Liquids MaterialDensity (gm cm -3 ) Water at 4 C1.0000 Water at 20 C0.998 Gasoline0.70 Mercury13.6 Milk1.03 Solids MaterialDensity (gm cm -3 ) Magnesium1.7 Aluminum2.7 Copper8.3-9.0 Gold19.3 Iron7.8 Lead11.3 Platinum21.4 Uranium18.7 Osmium22.5 Ice at 0 C0.92

5. B. Density Mass (g) Volume (cm 3 )

6. B. Density  Direct Proportion  Inverse Proportion y x y x

7. C. Measurement  Measurement is uncertain because  1. Instruments may have errors  2. Involves estimation Measurement = all certain digits + 1 uncertain digit (estimate)

8. Accuracy vs. Precision  Accuracy - how close a measurement is to the accepted value  Precision - how close a series of measurements are to each other ACCURATE = CORRECT PRECISE = CONSISTENT

9. D. Percent Error  Indicates accuracy of a measurement your value (observed value) accepted value

10. D. Percent Error  A student determines the density of a substance to be 1.40 g/mL. Find the % error if the accepted value of the density is 1.36 g/mL. % error = 2.9 %

11. E. Significant Figures  Indicate precision of a measurement.  Recording Sig Figs  Sig figs in a measurement include the known digits plus a final estimated digit 2.32 cm

12. Sig Fig Rules 1) ALL non-zero numbers (1,2,3,4,5,6,7,8,9) are ALWAYS significant. 2) ALL zeroes between non-zero numbers are ALWAYS significant. 3) ALL zeroes which are SIMULTANEOUSLY to the right of the decimal point AND at the end of the number are ALWAYS significant. 4) ALL zeroes which are to the left of a written decimal point and are in a number >= 10 are ALWAYS significant. (Helpful way to check rules 3 and 4 is to write the number in scientific notation. If you can/must get rid of the zeroes, then they are NOT significant.)

13. Sig Fig Examples Number# Significant FiguresRule(s) 48,92351 3.96741 900.0651,2,4 0.0004 (= 4 E-4)11,4 8.100051,3 501.04061,2,3,4 3,000,000 (= 3 E+6)11 10.0 (= 1.00 E+1)31,3,4

14. E. Significant Figures  Counting Sig Figs  Count all numbers EXCEPT:  Leading zeros -- 0.0025 what about:60.0025  Trailing zeros without a decimal point -- 2,500 what about: 2500.0

15. 4. 0.080 3. 5,280 2. 402 1. 23.50 E. 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

16. E. Significant Figures  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

17. E. Significant Figures  Calculating with Sig Figs (con’t)  Add/Subtract - The # with the lowest decimal value determines the place of the last sig fig in the answer. 3.75 mL + 4.1 mL 7.85 mL  7.9 mL 3.75 mL + 4.1 mL 7.85 mL 20.0685 + 4.25 24.3185 ??

18. F. Scientific Notation  Converting into Sci. Notation:  Move decimal until there’s 1 digit to its left. Places moved = exponent.  Large # (>1)  positive exponent Small # (<1)  negative exponent  Only include sig figs. 65,000 kg  6.5 × 10 4 kg

19. F. 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