Measurement in ScienceMeasurement in Science

Scientific Observation…

Empirical knowledge is gained by conducting experiments and making observations. There are 2 types of observations that can be gathered from experiments.

Qualitative Observations: Describe the features of an object or substance using the senses. Ex: Colour, gas bubbles, odour, precipitate.

Quantitative Observation: requires some sort of measuring equipment, usually numerical with a unit. Ex: Temperature, Volume, pH.

Measurement – A Quantitative Observation

• Measured results are required for quantitative observations.• Various factors will affect your confidence in your measured

results. Such as…

– Type of measuring equipment used– Amount to be measured (too large or too small)– Condition of equipment

All these factors must be minimized and controlled in order to increase confidence and decrease “uncertainty” in your measurements

The International System of Units

Length meter m

Mass kilogram kg

Time second s

Amount of substance mole mol

Thermodynamic temperatureKelvin K

Electric current amperes amps

Luminous intensity candela cd

Quantity Name Symbol

Dorin, Demmin, Gabel, Chemistry The Study of Matter , 3rd Edition, 1990, page 16

Prefixes in the SI System

Power of 10 for Prefix Symbol Meaning Scientific Notation_______________________________________________________________________

mega- M 1,000,000 106

kilo- k 1,000 103

deci- d 0.1 10-1

centi- c 0.01 10-2

milli- m 0.001 10-3

micro- 0.000001 10-6

nano- n 0.000000001 10-9

The Commonly Used Prefixes in the SI System

Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 118

Laboratory Equipmentused for accurate measurements

Burette GraduatedCylinder

PipetteVolumetricFlask

Laboratory Equipmentused for approximate measurements

Beaker ErlenmeyerFlask

Units of Measuring Volume

1 L = 1000 mL

Timberlake, Chemistry 7th Edition, page 3

Reading a Meniscus

The graduated cylinder on the left has scale marks 0.1 mL apart, so it can be read to the nearest 0.01 mL.

Reading across the bottom of the meniscus, a reading of 5.72 mL is reasonable (5.73 mL or 5.71 mL are acceptable, too).

Accuracy vs. PrecisionCertainty of Measurements

•Accuracy refers to the ability of the measurement to match the “true” value. How close are you to the real number?

•Precision refers to the ability of a measurement to be consistently reproduced

Accuracy vs. Precision

Random errors: reduce precision

Good accuracyGood precision

Poor accuracyGood precision

Poor accuracyPoor precision

Systematic errors: reduce accuracy

• Example: At STP, 5mL of pure water should have a mass of exactly 5 grams. The following students weighed a cylinder containing 5mL of pure water three times. Comment on their accuracy and precision:

Student A Student B Student C

5.0g 6.2g 6.4g

5.1g 6.1g 5.9g

4.9g 6.2g 4.2g

Estimating the last digit in measurements:

• The maximum possible precision of a measurement is 1/10 (0.1) times the smallest division on the measuring instrument

• Eg. If your ruler’s smallest division is the tenth’s place, your measurement should be to the hundredths place

• If your ruler’s divisions are to the one’s, you estimate to the tenth’s.

Rules for Rounding

1. If the last digit to be removed is…a. less than 5, the preceding digit stays the same.

For example, 1.33 round to 1.3.b. equal to or greater than 5, the preceding digit is

increased by 1.For example, 1.36 rounds to 1.4, and 3.15 rounds to 3.2.

If you have more than one step in a calculation, do not round until you arrive at the final answer!!!

Significant Digits

• Significant figures are used to show the accuracy of a measurement.

• All measurements consist of a number of digits about which we are certain, and a final digit that has been estimated.

• The expression of this measurement must show this certainty 

RULES FOR SIGNIFICANT DIGITS

1. All non-zero digits are significant. (Ex. 367 has 3 sigfigs)

2. All zeros between non-zero digits are significant. (Ex 307 has 3 sfs)

3. Zeros to the right of the last number smaller than one are significant. (Ex. 0.300 has 3 sfs)

4. All zeros to the right of the last whole number are not considered significant unless measured directly by the measuring device. (Ex. 6400 km has 2 sfs; 70. g has 2 sfs; 32.00 has 4 sfs)

5. All zeros to the left of a number less than one, are not significant. (Ex. 0.012 g has 2sfs)

6. Exact numbers (numbers derived from counting) are not considered measurements. When multiplying or dividing an uncertain value by an exact number, the answer has the same place setting as the measured value. (Ex. 3 x 14.7 mL will be expressed to the tenth)

SIGNIFICANT DIGITS IN CALCULATIONS

7. When adding or subtracting, the answer is expressed to the same place setting as the quantity with the highest place setting, which means round off your answer to the least number of decimals in the problem.

8. When multiplying or dividing, the answer should be rounded off to the same number of significant digits as the number having the fewest significant digits.

State the number of significant digits in the following:

a) 0.00123 g

b) 205 000 g

c) 370.0 g

d) 560. g

e) 1.23x104 g