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

• 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)

Units of Measurement

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?

xxxxx xx

x

x

x

x

xx

x xxxx

xx x

Precise but not accurate Accurate but not precise Accurate and precise

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

1. State given information

2. State unit plan

3. State equality and conversion factors

4. Set up calculation

5. Cancel units and calculate answer

6. Correct sig. figs.

Example Unit Conversion Problem• A marathon is 26.2 miles long. How long is

it in kilometers?

1. Marathon = 26.2 miles

2. mi km

3. 1 km = 0.621 mi so, 1 km/0.621 mi

4. 26.2 mi x 1 km/0.621 mi = km

5. 26.2 mi x 1 km/0.621 mi = 42.19001 km

6. Correct sig. figs. = 42.2 km

Temperature Conversions• Three temperature scales are Fahrenheit, Celsius

and Kelvin

F = 1.8C + 32

C = F - 32(0.555)

• K = C + 273.15

• For example:

Dry ice at -56.5C is at -69.7F 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