Chapter 1: Measurements

1. Chapter 1: Measurements

2. Chapter 1 Goals • Learn the units and abbreviations for the metric (SI) system • Measured or exact number? • Numbers in scientific notation • Accuracy and precision • Significant figures • The use of prefixes to change base units • Conversion factors • Calculating temperature in Celsius, Fahrenheit, and Kelvin

3. Metric (SI) System • Decimal system based on 10 • Used in most of the world (NOT U.S.!) • Used by hospitals and scientists Know: • Metric (SI) units for length, volume, mass and temperature

4. Units of Measurement * Metric (SI) units in bold

5. Measured Numbers: Device Uncertainty and error in measurement An apple is measured to be roughly 486g on a top loading balance Exact Numbers: From definition or counting items The number of apples in a sack is exactly 6 There are exactly 12 inches in a foot Measured and Exact Numbers

6. Measured Numbers 2 3 4 . l. . . . l . . . . l . . . . l . . . . l . . cm • To measure the length of the red line, we read the markings on the meter stick. The first digit 2 plus the second digit 2.7 • Estimating the third digit between 2.7–2.8 gives a final length reported as 2.75cm or 2.76cm

7. Scientific Notation • Large Numbers: 12,000,000 = 1.2 x 107 • Small Numbers: 0.00000012 = 1.2 x 10-7 • Short hand: Mass of a proton = 1.67 x 10-27 kg • Easier to determine magnitude: 0.00000000000000000000000000167 kg

8. Scientific Notation • A number in scientific notation contains a coefficient and a power of 10. coefficient power of ten coefficient power of ten 1.5 x 102 7.35 x 10-4 • Place the decimal point after the first digit. Indicate the spaces moved as a power of ten. 52 000 = 5.2 x 104 0.00378 = 3.78 x 10-3 4 spaces left 3 spaces right

9. Accuracy and Precision • Accuracy - close to the actual value • Precision - repeatability Example: 3 darts are precise, but not accurate!

10. Significant Figures • Significant figures -all the reported numbers including the estimated digit in measured numbers only (not exact) • All measured values have error • Significant figures are used to track digits of importance through calculations • Good explanation of sig figs is given on page 10 (table 1.3)

11. Counting Sig Figs • All non-zero digits are significant • Zeroes may or may not be significant Significant: • Sandwiched between two non-zero digits (607 m or 3.062 in) • At the end of a decimal (80. L or 65.0 ºC) • Any digit in the coefficient of a number in sci. not. (5.50 x 103 m or 4.00 x 10-2 g) Not significant: • At the beginning of a decimal number (small number) (0.0005 m or 0.015 g) • Used as a place holder for a large number without a decimal (530,000 m2 or 1,250,000 g)

12. Examples Significant figures? a.) 8.00 x 102 m b.) 0.00002 L c.) 600. in d.) 20.60 mL e.) 54,000 cm

13. Examples Significant figures? a.) 8.00 x 102 m - 3 sig figs b.) 0.00002 L - 1 sig fig c.) 600. In - 3 sig figs d.) 20.60 mL - 4 sig figs e.) 54,000 cm - 2 sig figs

14. Examples Scientific notation? a.) 60,800,000 sec (4sig figs) b.) 0.00820 ft (2 sig figs) c.) 0.00000345 L (3 sig figs) d.) 2600 mL (3 sig figs)

15. Examples Scientific notation? a.) 60,800,000 sec (4 sig figs) - 6.080 x 107 sec b.) 0.00820 ft (2 sig figs) - 8.2 x 10-3 ft c.) 0.00000345 L (3 sig figs) - 3.45 x 10-6 L d.) 2600 mL (3 sig figs) - 2.60 x 103 mL

16. Sig Figs in Calculations • Rounding off: • If first digit dropped is 4 or less the number is rounded down. If it is 5 or more the number is rounded up 8.4234  8.42 (3 sig figs) or 8.4 (2 sig figs) 14.780  14.8 (3 sig figs) or 15 (2 sig figs) • Multiplication and Division: • The number with the lesser amount of sig figs determines the sig figs in the answer 34.6 x 0.54 = 0.27804  0.28 (rounded to 2 sig figs) 67.2

17. Sig Figs in Calculations • Addition and Subtraction: • The number with the lesser amount of decimal places is used to determine decimal places in the answer 5.048 + 45.1 = 50.148  50.1 (1 decimal place)

18. Metric and SI System Prefixes

19. Metric and SI System Prefixes 1000g = 1 kilogram (kg) or 1g = 0.001kg 1m = 100centimeter (cm) or 0.01m = 1cm 1L = 1000milliliters (mL) or 0.001L = 1mL

20. Volume and Converting Cubic Units • 1000 mL = 1 L • 1 mL = 1 cm3 = 1 cc • 100 cm = 1 m • 100 cm3 IS NOT = 1 m3 • (1m)3 = (100 cm)3 = 1,000,000 cm3

21. Conversion Factors • Used for converting units and used A LOT in chemistry! • Step 1 – Identify information given • Step 2 – Plan how to reach desired units • Step 3 – Select necessary conversion factors • Step 4 – Set up conversions so they cancel • Step 5 – Solve problem and determine sig figs* • Unit should cancel leaving you with desired units

22. Example During surgery, a patient receives 5.0 pints of plasma. How many milliliters of plasma were given? 1 quart = 2pints

23. Example step 1: Given 5.0 pints step 2: pints  quarts  milliliters step 3:1 quart = 2pints and 1 quart = 946mL and step 4:

24. Density • The relationship between mass and volume • Density can be used as a conversion factor • Specific gravity is unitless but roughly equal to density numerically

25. Temperature • Measures how hot or cold things are • Measure in Fahrenheit, Celcius and Kelvin scales • Can NOT be converted simply using conversion factors • Different freezing temps for each scale