Conversions and Conversions and Significant FiguresSignificant Figures

Kelley KuhnKelley KuhnCenter for Creative ArtsCenter for Creative Arts

Dimensional AnalysisDimensional Analysis►One unit can be converted to another One unit can be converted to another

by using a conversion factor. by using a conversion factor. ►(Unit A)(conversion factor) = Unit B(Unit A)(conversion factor) = Unit B►Conversion factors are created by using the Conversion factors are created by using the

expression that expresses the relationship expression that expresses the relationship between the two units. For example:between the two units. For example: 1 foot = 12 inches, so the conversion factor1 foot = 12 inches, so the conversion factor

will be will be 1foot1foot or or 12 inches12 inches 12 in 1 foot12 in 1 foot

The correct choice shall be the one that The correct choice shall be the one that allows for the cancellation of the units.allows for the cancellation of the units.

Practice ConversionsPractice Conversions►Convert the following quantities from Convert the following quantities from

one unit to another using the following one unit to another using the following relationships.relationships.

► 1 m = 1.094 yd1 m = 1.094 yd 1 mile = 1760 yd1 mile = 1760 yd 1 kg = 2.205 lbs1 kg = 2.205 lbs►30 m to mil30 m to mil►1500 yd to mil1500 yd to mil►206 mil to m206 mil to m►34 kg to lbs34 kg to lbs►34 lb to kg34 lb to kg

DensityDensityDensity is an important physical characteristic in Density is an important physical characteristic in

Chemistry. It is often used to aid in the Chemistry. It is often used to aid in the identification of unknown solids and liquids.identification of unknown solids and liquids.

Density = mass/volumeDensity = mass/volume Because liquids are frequently used in the lab Because liquids are frequently used in the lab

setting, a volume measured in graduated setting, a volume measured in graduated cylinder can be used to determine the mass cylinder can be used to determine the mass using density.using density.

Mass = (density)(volume)Mass = (density)(volume)

““Certainty” in MeasurementCertainty” in Measurement►When visually reading the When visually reading the

measurement using a lab tool such as measurement using a lab tool such as a graduated cylinder or meter stick, a graduated cylinder or meter stick, there is always a certain degree of there is always a certain degree of uncertainty in the recorded quantity. uncertainty in the recorded quantity. The reading may fall between two The reading may fall between two divisions on the scale and an estimate divisions on the scale and an estimate must be made in order to record the must be made in order to record the final digit. final digit.

Example of UncertaintyExample of Uncertainty When reading a graduated cylinder, the When reading a graduated cylinder, the

lowest point on the curve of the liquid is lowest point on the curve of the liquid is read as the volume. What is the volume of read as the volume. What is the volume of this liquid?this liquid?

meniscus

20

15

Because the eye can discriminate the approximate distance between the 17th and 18th mls, this number must be recorded and is said to be uncertain. The actual volume would be recorded as 17.3 mls +/- .2 mls.

Are Significant Figures Important? A Are Significant Figures Important? A FableFable

► A student once needed a cube of metal which had to have a mass of 83 grams. A student once needed a cube of metal which had to have a mass of 83 grams. He knew the density of this metal was 8.67 g/mL, which told him the cube's He knew the density of this metal was 8.67 g/mL, which told him the cube's volume. Believing significant figures were invented just to make life difficult for volume. Believing significant figures were invented just to make life difficult for chemistry students and had no practical use in the real world, he calculated the chemistry students and had no practical use in the real world, he calculated the volume of the cube as 9.573 mL. He thus determined that the edge of the cube volume of the cube as 9.573 mL. He thus determined that the edge of the cube had to be 2.097 cm. He took his plans to the machine shop where his friend had had to be 2.097 cm. He took his plans to the machine shop where his friend had the same type of work done the previous year. The shop foreman said, "Yes, we the same type of work done the previous year. The shop foreman said, "Yes, we can make this according to your specifications - but it will be expensive." can make this according to your specifications - but it will be expensive."

► "That's OK," replied the student. "It's important." He knew his friend has paid "That's OK," replied the student. "It's important." He knew his friend has paid $35, and he had been given $50 out of the school's research budget to get the $35, and he had been given $50 out of the school's research budget to get the job done. job done.

► He returned the next day, expecting the job to be done. "Sorry," said the He returned the next day, expecting the job to be done. "Sorry," said the foreman. "We're still working on it. Try next week." Finally the day came, and foreman. "We're still working on it. Try next week." Finally the day came, and our friend got his cube. It looked very, very smooth and shiny and beautiful in its our friend got his cube. It looked very, very smooth and shiny and beautiful in its velvet case. Seeing it, our hero had a premonition of disaster and became a bit velvet case. Seeing it, our hero had a premonition of disaster and became a bit nervous. But he summoned up enough courage to ask for the bill. "$500, and nervous. But he summoned up enough courage to ask for the bill. "$500, and cheap at the price. We had a terrific job getting it right -- had to make three cheap at the price. We had a terrific job getting it right -- had to make three before we got one right." before we got one right."

► "But--but--my friend paid only $35 for the same thing!" "But--but--my friend paid only $35 for the same thing!" ► "No. He wanted a cube 2.1 cm on an edge, and your specifications called for "No. He wanted a cube 2.1 cm on an edge, and your specifications called for

2.097. We had yours roughed out to 2.1 that very afternoon, but it was the 2.097. We had yours roughed out to 2.1 that very afternoon, but it was the precision grinding and lapping to get it down to 2.097 which took so long and precision grinding and lapping to get it down to 2.097 which took so long and cost the big money. The first one we made was 2.089 on one edge when we got cost the big money. The first one we made was 2.089 on one edge when we got finshed, so we had to scrap it. The second was closer, but still not what you finshed, so we had to scrap it. The second was closer, but still not what you specified. That's why the three tries." specified. That's why the three tries."

► "Oh!" "Oh!"

Significant FiguresSignificant Figures►The certain and uncertain numbers that The certain and uncertain numbers that

must be recorded are called significant must be recorded are called significant figures. figures.

►Significant figures (sigfigs) are important Significant figures (sigfigs) are important for accurately conveying experimental for accurately conveying experimental data.data.

►Sigfig rules help to identify which Sigfig rules help to identify which numbers have meaning and which are numbers have meaning and which are simply placeholders. simply placeholders.

Significant Figure RulesSignificant Figure Rules► All non-zero integers are counted as significant figures.All non-zero integers are counted as significant figures.► Leading zeros are those that precede all of the non-zero Leading zeros are those that precede all of the non-zero

integers and are NEVER counted as significant figures.integers and are NEVER counted as significant figures.► Captive zeros are those that fall between non-zero digits Captive zeros are those that fall between non-zero digits

and are ALWAYS counted as sigfigs.and are ALWAYS counted as sigfigs.► Trailing zeros are those at the end of a number and ONLY Trailing zeros are those at the end of a number and ONLY

significant if the number is written with a decimal.significant if the number is written with a decimal.► EXACT numbers have an unlimited number of significant EXACT numbers have an unlimited number of significant

figures. (Exact numbers are those which are a result of figures. (Exact numbers are those which are a result of counting or by definition, such as 1kg = 2.205 lbs.)counting or by definition, such as 1kg = 2.205 lbs.)

► In scientific notation, the 10In scientific notation, the 10xx part is NEVER significant. part is NEVER significant.

Using Sigfigs in CalculationsUsing Sigfigs in Calculations►When When multiplyingmultiplying or or dividingdividing, limit the , limit the

answer to the same number of answer to the same number of significant significant figuresfigures that appear in the original data that appear in the original data with the fewest number of sigfigs.with the fewest number of sigfigs.

►When When addingadding or or subtractingsubtracting, limit the , limit the answer to the same number of answer to the same number of decimal decimal placesplaces that appear in the original data that appear in the original data with the fewest number of decimal with the fewest number of decimal places.places.

Let’s Try It!Let’s Try It!►How many sigfigs in these numbers?How many sigfigs in these numbers?

0.00970, 130400, 0.203040, 7.650 x 100.00970, 130400, 0.203040, 7.650 x 10-8-8

3, 4, 6, 43, 4, 6, 4

Record the answer to the following in Record the answer to the following in correct sigfigs.correct sigfigs.

10.045 + .3310.045 + .33 .00976 – 0.0100.00976 – 0.0100(34.00)(0.001)(34.00)(0.001) 76.2/0.100076.2/0.1000