Observations

• QualitativeObserved 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 inches1 yard = 3 feet

Volume: 1 gallon = 4 quarts1 quart = 2 pints = 32 ounces1 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 AnalysisFactor-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

OR1 m = 1000 mm1m 1 m

1m = 1 = 1000 mm1000mm 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

Copyright © 2001 The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Significant FiguresFigure TA 1.2

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