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Chapter 1: Measurements

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

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

Units of Measurement PropertyMetric UnitUS UnitConversion LengthMeter (m)Inch (in)1m = 39.4 in 1in = 2.54 cm VolumeLiter (L) Cubic meter (m 3 ) Quart (qt)1L = 1.06 qt 1qt = 946 mL MassGram (g) Kilogram (kg) Pound (lb)1kg = 2.20 lb 1lb = 454 g TempCelsius (ºC) Kelvin (K) Fahrenheit (ºF)0 ºC, 32ºF, and 273K * Metric (SI) units in bold

Measured and Exact Numbers 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

. 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 2.75 cm or 2.76 cm Measured Numbers 2 3 4

Scientific Notation Large Numbers: 12,000,000 = 1.2 x 10 7 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

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 10 2 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 10 4 0.00378 = 3.78 x 10 -3 4 spaces left 3 spaces right

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

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)

Counting Sig Figs 1.All non-zero digits are significant 2.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 10 3 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 m 2 or 1,250,000 g)

Examples Significant figures? a.) 8.00 x 10 2 m b.) 0.00002 L c.) 600. in d.) 20.60 mL e.) 54,000 cm

Examples Significant figures? a.) 8.00 x 10 2 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

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)

Examples Scientific notation? a.) 60,800,000 sec (4 sig figs) - 6.080 x 10 7 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 10 3 mL

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

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)

Metric and SI System Prefixes PrefixAbbreviationConversion Mega M1,000,000 Kilo k1,000 -- 1 Centi c1/100 Milli m1/1,000 Micro µ1/1,000,000

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

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

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

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

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

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

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

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