Measurement

Scientific Notation

• Rules for Working with Significant Figures: 1. Leading zeros are never significant.

2. Imbedded zeros are always significant. 3. Trailing zeros are significant only if the decimal point is specified. Hint: Change the number to scientific notation. It is easier to see.

Scientific Notation

• Addition or Subtraction:The last digit retained is set by the first doubtful digit.

• Multiplication or Division:The answer contains no more significant figures than the least accurately known number.

ExamplesExample Number of

Significant Figures

Scientific Notation

0.00682 3 6.82 x 10-3 Leading zeros are not

significant.

1.072 4 1.072 (x 100) Imbedded zeros are

always significant.

300 1 3 x 102 Trailing zeros are significant

only if the decimal point is specified.

300. 3 3.00 x 102

300.0 4 3.000 x 102

ExamplesAddition Even though your

calculator gives you the answer 8.0372, you must round off to 8.04. Your answer must only contain 1 doubtful number. Note that the doubtful digits are underlined.

Subtraction Subtraction is interesting when concerned with significant figures. Even though both numbers involved in the subtraction have 5 significant figures, the answer only has 3 significant figures when rounded correctly. Remember, the answer must only have 1 doubtful digit.

Examples

Multiplication The answer must be rounded off to 2 significant figures, since 1.6 only has 2 significant figures.

Division The answer must be rounded off to 3 significant figures, since 45.2 has only 3 significant figures.

Rounding• When rounding off numbers to a certain number of significant figures, do so to the

nearest value. – example: Round to 3 significant figures: 2.3467 x 104 (Answer: 2.35 x 104)

– example: Round to 2 significant figures: 1.612 x 103 (Answer: 1.6 x 103)

• What happens if there is a 5? There is an arbitrary rule: – If the number before the 5 is odd, round up.

– If the number before the 5 is even, let it be. The justification for this is that in the course of a series of many calculations, any rounding errors will be averaged out.

– example: Round to 2 significant figures: 2.35 x 102 (Answer: 2.4 x 102)

– example: Round to 2 significant figures: 2.45 x 102 (Answer: 2.4 x 102)

– Of course, if we round to 2 significant figures: 2.451 x 102, the answer is definitely 2.5 x 102 since 2.451 x 102 is closer to 2.5 x 102 than 2.4 x 102.

Measurement • A rule of thumb: read the volume to 1/10 or 0.1 of the

smallest division. (This rule applies to any measurement.) This means that the error in reading (called the reading error) is 1/10 or 0.1 of the smallest division on the glassware.

• The volume in this beaker is 47 1 mL. You might have read 46 mL; your friend might read the volume as 48 mL. All the answers are correct within the reading error of 1 mL.

Accuracy v. Precision

accurate(the

average is accurate)

not precise

precisenot

accurate

accurateand

precise

Accuracy refers to how closely a measured value agrees with the correct value.Precision refers to how closely individual measurements agree with each other.

                                                               

Metric System

LENGTH

Unit Abbreviation Number of Meters

Approximate U.S. Equivalent

kilometer km 1,000 0.62 mile

hectometer hm 100 328.08 feet

dekameter dam 10 32.81 feet

meter m 1 39.37 inches

decimeter dm 0.1 3.94 inches

centimeter cm 0.01 0.39 inch

millimeter mm 0.001 0.039 inch

micrometer µm 0.000001 0.000039 inch

Metric System

VOLUME

Unit Abbreviation Number of Cubic Meters

Approximate U.S. Equivalent

cubic meter m3 1 1.307 cubic yards

cubic decimeter dm3 0.001 61.023 cubic inches

cubic centimeter cu cm orcm3 also cc 0.000001 0.061 cubic inch

Metric SystemCAPACITY

Unit Abbreviation Number of Liters Approximate U.S. Equivalent

cubic dry liquid

kiloliter kl 1,000 1.31 cubic yards

hectoliter hl 100 3.53 cubic feet 2.84 bushels

dekaliter dal 10 0.35 cubic foot 1.14 pecks 2.64 gallons

liter l 1 61.02 cubic inches 0.908 quart 1.057 quarts

cubic decimeter dm3 1 61.02 cubic inches 0.908 quart 1.057 quarts

deciliter dl 0.10 6.1 cubic inches 0.18 pint 0.21 pint

centiliter cl 0.01 0.61 cubic inch 0.338 fluid ounce

milliliter ml 0.001 0.061 cubic inch 0.27 fluid dram

microliter µl 0.000001 0.000061 cubic inch

0.00027 fluid dram

Metric System

MASS AND WEIGHT

Unit Abbreviation Number of Grams

Approximate U.S. Equivalent

metric ton t 1,000,000 1.102 short tons

kilogram kg 1,000 2.2046 pounds

hectogram hg 100 3.527 ounces

dekagram dag 10 0.353 ounce

gram g 1 0.035 ounce

decigram dg 0.10 1.543 grains

centigram cg 0.01 0.154 grain

milligram mg 0.001 0.015 grain

microgram µg 0.000001 0.000015 grain

Dimensional Analysis

• Dimensional Analysis is a problem-solving method that uses the fact that any number or expression can be multiplied by one without changing its value.

Dimensional Analysis

• How many centimeters are in 6.00 inches?

• Express 24.0 cm in inches.

Dimensional Analysis

• How many seconds are in 2.0 years?

Mass v. Weight• 1) Mass is a measurement of the amount of matter

something contains, while Weight is the measurement of the pull of gravity on an object.

• 2) Mass is measured by using a balance comparing a known amount of matter to an unknown amount of matter. Weight is measured on a scale.

• 3) The Mass of an object doesn't change when an object's location changes. Weight, on the other hand does change with location.

Volume

• The amount of space occupied by an object• 1 L = 1000 mL = 1000 cm 3

• 1 L = 1 cm 3

• 1 L = 1.0.57 qt• 946.1 ml = 1 qt

Temperature

• Measure of intensity of thermal energy

• What does this mean? How hot a system is…

Conversion Formulas

Density

• Physical characteristic• Used to id a substance• d =m/v