Observations Qualitative Quantitative (measurements) Two parts needed Observed directly Color, texture, magnetic, state of matter, etc Quantitative (measurements) Two parts needed Number AND unit (Naked numbers are meaningless)

Examples of Units

Why do we need standard units?

Units English system “unrelated” units 1 ft = 12 in Metric system Units related by powers of 10 Units can be made larger or smaller with prefixes

English System Mass: 1 pound = 16 ounces Length: 1 foot = 12 inches 1 yard = 3 feet Volume: 1 gallon = 4 quarts 1 quart = 2 pints = 32 ounces 1 pint = 2 cups

Metric System Mass: gram (g) Length: meter (m) Volume: liter (L)

Need to know: Metric Prefixes English system relationships Useful relationships for converting between systems

Converting between units Dimensional Analysis Factor-Label Method 1. Within same system 2. Between systems BOTH require a conversion factor

Metric System Can change size of the unit by applying a prefix 1 kilometer (km) = 1000 meters (m) kilo = 1000

Conversion factor Convert from millimeters (mm) to meters (m) Start with equivalence statement 1 m = 1000 mm Can divide to get conversion factor

1 m = 1000 mm 1000mm 1000 mm OR 1 m = 1000 mm 1m 1 m 1m = 1 = 1000 mm 1000mm 1m Can always multiply something by “1” safely

Converting from one unit to another How many km are there in 200 m? Have m Want km Know 1 km = 1000 m 200m x 1 km = 0.200 km 1000m Use conversion factor that will let units cancel to give wanted unit

Does your answer make sense? How many km are there in 200 m? Going from m (a small unit) to km (larger unit), so we should have fewer km than m Answer: 0.200 km (fewer km than m)

200m x 1 km = 0.200 km 1000m Which conversion factor do we want? Units to be cancelled on bottom Units wanted on top

Converting between systems Set up same way, except that you need a conversion (bridging) unit between the two systems 1 lb = 454 g How many pounds are there in 114 grams?

114 g x 1 lb = 0.25 lb 454g

Uncertainty in Measurements Measurement is only as good as the “measuring” instrument Must choose an appropriate device To weigh your cat, should you use a truck weigh station or a baby scale? Why?

The number of digits that you can actually “count” for a real measurement depends upon the measuring device. Includes all measured number plus one “uncertain” last digit, which is estimated Can only estimate one place beyond the lines or marks

Significant figures - all digits in a number representing data or results that are known with certainty plus one uncertain digit.

Suppose that two people read the bottom ruler and get measurements of 5.36 cm and 5.37 cm. Which one is the correct reading?

5.4 cm +/- 0.1 cm (5.3 – 5.5 cm) 5.36 cm +/- 0.01 cm (5.35-5.37 cm) Which has less uncertainty? 5.4 (ca 2%) 5.36 (ca 0.2%)

Uncertainty in Measurements Measuring device determines uncertainty and number of significant digits (numbers that have meaning)

Accuracy and Precision Accuracy: How close measurements are to actual value Precision: How close measurements are to each other

Figure: 01-25