Measurement Used in everyday life: cooking, taking your temperature Also used extensively in chemistry: mass, volume, etc. Gives you a way to make quantitative observations about the world around you

Observations Qualitative = What is it? Quantitative = How much? Quantitative observations (measurements) always include a Number plus a Unit - 4 inches - 1 pound

Units of Measurement US system, metric and SI Metric is most common in science and medicine Know US and Metric units for: - Length (feet, meters) - Volume (quarts, liters) - Mass (pounds, grams) -Temperature (Fahrenheit, Celsius)

Measuring Length When making measurements, estimate one digit farther than the finest markings

Measuring Volume When measuring volume, always read at the bottom of the meniscus Remember to estimate one digit farther than the finest markings

Measuring Mass When measuring mass, record all of the digits provided by the scale

Measuring Temperature Again, remember to estimate one digit more than the finest markings on the thermometer

Metric Prefixes Use a prefix to relate a unit to its base unit Base unit for length is the meter, and kilo = 1000, so 1 kilometer = 1000 meters Know metric prefixes and abbreviations for metric units ( 1 kilometer = 1 km) Use the correct abbreviations for units so that you don’t mix them up

Scientific Notation Scientific notation is used to write large or small numbers 1000 = 1 x 103 0.001 = 1 x 10-3 Scientific notation has a coefficient times a power of 10, where the coefficient is a number from 1 to less than 10 Learn to use scientific notation on your calculator

Measured and Exact Numbers When measuring, the last digit is estimated by reading between the smallest divisions Therefore, measured numbers have uncertainty Exact numbers have no uncertainty Exact numbers come from counting whole objects, or from definitions: - There are 33 people in this room - 100 cm = 1 m

Accuracy vs. Precision Accuracy = How close to the true value? Precision = How repeatable is the measured value?

Significant Figures All reported digits in measured numbers are significant (including the estimated one) Sig. Figs. are a measure of uncertainty More sig. figs. = less uncertainty For numbers ending in zero, it’s best to use scientific notation to indicate sig. figs.: 500 = 5 x 102 vs. 500. = 5.00 x 102

Sig. Figs. in Measurements

Sig. Figs. In Calculations For adding and subtracting: line up decimal places and use fewest decimal places in answer 5.28 + 3.1 + 4.002 = 12.382 on calculator Correct sig. figs. = 12.4 For multiplying and dividing: use least sig. figs. in answer 2.3 x 1.11 = 2.553 on calculator Correct sig. figs. = 2.6 Always carry all decimal places through multi-step calculations and then adjust sig. figs. at end

Unit Conversions To convert from one unit to another, a conversion factor is used The conversion factor comes from an equality Example: 1 kg = 1000 g can become 1 kg/1000 g or 1000 g/1 kg

Solving Unit Conversion Problems State given information State unit plan State equality and conversion factors Set up calculation Cancel units and calculate answer Correct sig. figs.

Example Unit Conversion Problem A marathon is 26.2 miles long. How long is it in kilometers? Marathon = 26.2 miles mi  km 1 km = 0.621 mi so, 1 km/0.621 mi 26.2 mi x 1 km/0.621 mi = km 26.2 mi x 1 km/0.621 mi = 42.19001 km Correct sig. figs. = 42.2 km

Temperature Conversions Three temperature scales are Fahrenheit, Celsius and Kelvin F = 1.8C + 32 C = F - 32(0.555) K = C + 273.15 For example: Dry ice at -56.5C is at -69.7F and is at 216.7 K

Percent Calculations % = (part/whole) x 100% Percent can be used as a conversion factor 20% can be 20/100 or 100/20 Example: If wine is 13% alcohol (by volume), how many mL of alcohol are in 125 mL of wine? (125 mL wine) x (13 mL alcohol/100 mL wine) = 16 mL alcohol

Density Density is a measure of how much mass there is per volume: d = m/V Helium is less dense than air, so a helium balloon floats Copper and zinc are more dense than water, so a penny sinks in the wishing well Density can be in any units of mass/volume (g/mL, g/L, kg/L etc.)

Densities of Some Common Substances

Indiana Jones Movie Example In the movie, Jones replaces a gold statue with sand in order to avoid setting off a deadly booby trap The density of gold = 19.32 kg/L and the density of sand = about 3 kg/L If the same volume of sand is used to replace the statue, will the booby trap be set off? Yes, gold is around 7 times as dense as sand, so you would have to use around 7 times the volume If the volume of the idol is 1.0 L (the idol is solid gold), what is its mass (in kg and in lb)? (1 kg = 2.20 lb) m = dV = (19.32 kg/L) x (1.0 L) = 19 kg 19 kg x 2.20 lb/1 kg = 43 lb

Density from Water Displacement Method When fully submerged, a solid object will displace its volume in water Volume of the water is measured before and after submerging the object - the volume difference = the volume of the object - the mass is measured and d = m/V