Name: Name: Name: Name: Worksheet 2 Units, Signifiant Figures, Dimensional Analysis, & Density Objeitives To recognize and use both S.I. and English units correctly. To be able to record a measurement to the correct precision and number of signifcant fgures. To be able to round the result of one or more operations to the correct precision and number of signifcant fgures. To know, understand, and be able to apply the principles of dimensional analysis to a wide variety of problems. To understand be able to use density. Signifiant Figures Every measured number has a certain precision, which means it has a limited number of signifcant fgures. When reading a number that came from a measurement all non zero digits count as signifcant fgures. Leading zeroes never count as signifcant fgures. Enclosed zeroes always count as signifcant fgures. Trailing zeroes count as signifcant fgures if and only if there is a decimal point specifcally shown in the number. Page 1 of 10
Rounding When rounding a number round the last signifcant digit up if the frst digit dropped is 5 or larger. If the frst digit dropped is less than 5 do not round up, leave the last signifcant fgure as is. When rounding the result of addition or subtraction round to the same place in the number as the last signifcant fgure is in the least precise of the numbers being added or subtracted. When rounding the result of multiplication or division round the result to the same number of signifcant fgures as the number with the least number of signifcant fgures. When performing mixed operations do each step in the order of operations, one at a time. Keep track of where you would round at each step, but do not actually round until after the last step. Fundamental S.I. Units Quantity Name Abbreviation Length Meter m Mass Kilogram kg Temperature Kelvin K Amount Mole mol Time Second s Electric Current Ampere A Luminous Intensity Candela cd Page 2 of 10
S.I. Prefies Prefi Symbol Meaning Deiimal Notation exa E x 10 18 1,000,000,000,000,000,000 peta P x 10 15 1,000,000,000,000,000 tera T x 10 12 1,000,000,000,000 giga G x 10 9 1,000,000,000 mega M x 10 6 1,000,000 kilo k x 10 3 1,000 hecto h x 10 2 100 deka da x 10 1 10 x 10 0 1 deci d x 10 1 0 centi c x 10 2 0.01 milli m x 10 3 0.001 micro m x 10 6 0.000001 nano n x 10 9 0.000000001 pico p x 10 12 0.000000000001 femto f x 10 15 0.000000000000001 atto a x 10 18 0.000000000000000001 Page 3 of 10
Unit (Eiait) Some Conversion Faitors Conversion 1 kilogram 2.2046 pounds 1 pound 453.59 grams 1 pound 16 ounces (exact) 1 ton 2000 pounds (exact) 1 metric ton 1000 kilograms (exact) 1 amu 1.66056 x 10 27 kg 1 ml 1 cm 3 (exact) 1 gallon 3.875 liters 1 liter 1.0567 quarts 1 gallon 4 quarts (exact) 1 gallon 8 pints (exact) 1 quart 32 fluid ounces (exact) 1 inch 2.54 cm (exact) 1 mile 5,280 feet (exact) Temperature Conversions Density Page 4 of 10
Dimensional Analysis 1.) Determine the units your answer will have. Write these on the left side of an equals sign. 2.) Determine your starting point (what is being converted into the units of your answer?). This will have a number as well as units. Write these on the right side of the equals sign. 3.) Determine which conversion factors you will need to convert from your starting point to the units of your answer. These may come from information given in the problem or relationships you are to memorize. Write each of these as an equality. 4.) Insert your conversion factors one at a time into your equation as fractions, ensuring that the units cancel out until you are left with the units of your answer (all other units should cancel). 5.) Calculate your result and round to the correct number of signifcant fgures. Problems Have one person in your group (who has neat handwriting) put down all of the work for each problem. Make sure to include units and round the fnal answer to the correct number of signifcant fgures. Put the fnal answer in the space provided. Use only the conversions provided above. Google NOTHING. 1.) The circumference of the earth at the equator is 25,000 mi. If the earth were a perfect sphere, what would be the volume of the earth in liters? The circumference of a sphere is given by where r is the radius of the sphere. The volume of a sphere is given as. _ Page 5 of 10
2.) A kettle has inner diameter of 17.50 inches and an inner height of 20.10 in. What is the volume of the kettle in gallons? Treat the kettle as a cylinder. where r is the radius of the cylinder and h is it s height. 3.) At what temperature is the temperature in o F equal numerically to the temperature in o C? Page 6 of 10
4.) How many grams of calcium sulfate dihydrate does it take to give 101 ppm (parts per million) of calcium in 11.5 gallons of water at room temperature? Take the density of the water as 1.00 g/ml. The are 40.0 grams of calcium in every 172 grams of calcium sulfate dihydrate. 5.) Convert 69.3 mi/h (miles per hour) to m/s (meters per second). Page 7 of 10
6.) The density of liquid mercury at room temperature is 13.59 g/ml. Convert this density to lb/ft 3. 7.) You measure water in two containers: a 10-mL graduated cylinder with marks at every 0.1 ml, and a burette marked at every 0.001 ml. If you have measure water in each of the containers and add them together, to what decimal place could you report the total volume of water? 8.) How many liters are there in 2.73 cubic yards (yd 3 )? Page 8 of 10
9.) The pressure of the earth's atmosphere at one point is 11.9 lb/in 2. What is the pressure when expressed in kg/m 2? 10.) On a new temperature scale ( Q), water boils at 142.3 Q and freezes at 72.5 Q. Calculate room temperature using this temperature scale. On the Celsius scale, normal room temperature could typically be 21.1 C. Water boils at 100.0 C and freezes at 0.00 C. Page 9 of 10
11.) A piece of niobium with a mass of 79.22 g is submerged in 39.22 ml of water in a graduated cylinder. The water level increases to 48.46 ml. Based on this data, what is the density of niobium? Page 10 of 10