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.

Examples ExampleNumber of Significant Figures Scientific Notation x Leading zeros are not significant (x 10 0 )Imbedded zeros are always significant x 10 2 Trailing zeros are significant only if the decimal point is specified x x 10 2

Examples AdditionEven though your calculator gives you the answer , you must round off to Your answer must only contain 1 doubtful number. Note that the doubtful digits are underlined. SubtractionSubtraction 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 MultiplicationThe answer must be rounded off to 2 significant figures, since 1.6 only has 2 significant figures. DivisionThe 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: x 10 4 (Answer: 2.35 x 10 4 ) – example: Round to 2 significant figures: x 10 3 (Answer: 1.6 x 10 3 ) 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 10 2 (Answer: 2.4 x 10 2 ) – example: Round to 2 significant figures: 2.45 x 10 2 (Answer: 2.4 x 10 2 ) – Of course, if we round to 2 significant figures: x 10 2, the answer is definitely 2.5 x 10 2 since x 10 2 is closer to 2.5 x 10 2 than 2.4 x 10 2.

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 precise not accurate accurate and 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 UnitAbbreviation Number of Meters Approximate U.S. Equivalent kilometerkm1, mile hectometerhm feet dekameterdam feet meterm inches decimeterdm inches centimetercm inch millimetermm inch micrometerµm inch

Metric System VOLUME UnitAbbreviation Number of Cubic Meters Approximate U.S. Equivalent cubic meterm3m cubic yards cubic decimeterdm cubic inches cubic centimeter cu cm or cm 3 also cc cubic inch

Metric System CAPACITY UnitAbbreviation Number of Liters Approximate U.S. Equivalent cubicdryliquid kiloliterkl1, cubic yards hectoliterhl cubic feet2.84 bushels dekaliterdal cubic foot1.14 pecks2.64 gallons literl cubic inches quart1.057 quarts cubic decimeterdm cubic inches quart1.057 quarts deciliterdl cubic inches0.18 pint0.21 pint centilitercl cubic inch fluid ounce milliliterml cubic inch0.27 fluid dram microliterµl cubic inch fluid dram

Metric System MASS AND WEIGHT UnitAbbreviation Number of Grams Approximate U.S. Equivalent metric tont1,000, short tons kilogramkg1, pounds hectogramhg ounces dekagramdag ounce gramg ounce decigramdg grains centigramcg grain milligrammg grain microgramµg 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 = qt 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