Easy Metric Conversions

MATHEMATICAL SKILLS YOU SHOULD HAVE MASTERED FROM HONORS CHEMISTRY I

YOU SHOULD BE ABLE TO:

1. Be able to take numbers in and out of scientific notation 2. Add, subtract, multiply, and divide numbers that are in scientific notation 3. Be able to convert numbers from one metric unit to another, using metric prefixes from MEMORY 4. Be able to convert numbers from one metric unit to another, when the numbers are in scientific notation – this involves just changing the exponent 5. Be able to convert between solid volume units and liquid volume units – for example, going between cm3 and mL, and more complex volume conversions as well 6. Be able to convert between a metric unit and an English unit (say between cm and inches) given the conversion factor using dimensional analysis 7. Be able to reduce down your final answer to a ratio over one to report your final answer – for example, an answer is not reported as 125 grams/25 mL, but rather, 5.0 g/mL. 8. Be able to keep track of units during the course of all of your calculations 9. Be able to recognize how many significant figures are in a number, and why that is important to the measurement 10. Be able to recognize that every number represents a real measurement in the practical world, and be able to tell what two numbers it would fall between on a measuring device 11. Be able to keep track of significant figures when you add, subtract, multiply, and divide, to obtain a final answer

WE WILL REVIEW SOME OF THESE CONCEPTS DURING VARIOUS LABS AND LECTURES THROUGHOUT THE COURSE OF THE YEAR – BUT YOU ARE ULTIMATELY RESPONSIBLE FOR THESE CONCEPTS! SEE ME IF YOU NEED HELP WITH THESE!!!! EASY CONVERSIONS! YEAH!

1. The mass of the earth is 5.98 x 1024 Kg. Convert this into dg. 2. There are 774,000 words in the Bible. Convert this into Megawords. 3. The average cow gives about 6400 liters of milk each year. Convert this into Hectoliters. 4. The slowest animal alive is the snail – it moves about .02 kilometers every hour. Convert this into decimeters. 5. The wind in Antarctica blows 129, 870 meters every hour. Convert this into millimeters. 6. You use 200 muscles every time you take one step. How many Dekamuscles is this? 7. The average soda bottle contains 2 liters of soda. Convert this into centiliters. 8. The width of a human hair is 80 micrometers (m). Convert this into decimeters. 9. Convert 5.50 inches into centimeters! 10. Convert 542 lbs into kilograms! 11. Convert 230.0 cm3 into Liters! 12. Convert 3.02 miles into kilometers! 13. Convert 320 feet into centimeters! 14. Convert 40 liters into quarts! 15. Convert 200,000 kg of water into liters of water! 16. Convert 4002 kg into pounds! 17. Convert 3200 kilometers into inches! 18. Convert 340 centimeters into inches! 19. How many seconds would be required for an object to move 25 meters if its speed is 50.0 m/s? 20. How far has an automobile traveled if it moves at 120 km per hour, and has been driving for 1.55 hours? 21. What is the volume of .700 Hgrams of ether if the density of ether is 0.70 g/ml? 22. An experiment requires 15.2 g of sugar per student in a class of 33 students who will be doing the lab. How many pounds of sugar are required for this lab assuming a15.0% excess? 23. A uniform steel bar is 16.0 inches long and weighs 6.25 lbs. Determine the mass of the bar in grams per centimeter of length. 24. A solution contains 500.0 cg of sodium hydroxide per liter. How many grams will be contained in 50.0 mL? 25. A solution contains 0.05 g of salt per milliliter. How many liters of this solution will be needed if we are to get 100.0 g of salt? 26. If gold contains 19.3 grams per cm3, how many kilograms would 340.0 cm3 of gold mass out to be? 27. A satellite is orbiting the earth at a speed of 18,000 miles per hour. What is the time in seconds that it takes to travel 100.0 miles? 28. First class postage is 25 cents for each ounce or fraction thereof. How much postage is required for a letter weighing 98.0 g? 29. The most abundant element in seawater is chlorine. Seawater contains 19,000 mg of chlorine per liter. Calculate this as g / m3. 30. The average density of the total earth is 5.52 g/cm3. Convert to kg/m3. 31. The United States has produced more than 380,000 metric tons of Al per month. If the density of Al is 2.70 g per cm3, how many m3 is this? 32. It is estimated that in the aurora borealis, excited hydrogen atoms in the atmosphere may travel 2000 km per second. Convert to miles/hour. 33. A 32 fluid-ounce (946 ml) can of fruit juice contains an artificial sweetener, calcium saccharin. The concentration is 7.5 mg sweetener per fluid ounce. Express this concentration in milligrams per milliliter. 34. A certain city uses 30,000 kl of water per day. How many metric tons of water are used in 1 year? Assume 365 days per year. There are 1000.0 kg per metric ton.

CONVERSIONS – THESE ARE ALL EXACT MEASUREMENTS: 2.54 cm = 1 inch, 2.2 lbs = 1 kg, 1.61 km = 1 miles, 3.79 liters = 1 gallon, 4 quarts = 1 gallon, 12 inches = 1 ft, 5280 ft = 1 miles, 1 pound = 454 grams 1 oz = 28.4 grams SOME EASY CONVERSIONS! YEAH!

1. Abie Goldberry, a Quebec junior hockey player from the 1930's was hit by a puck while playing hockey, which ignited a set of matches that he had in his pocket. His uniform caught on fire and he was burned quite badly before the fire was put out 6.00 minutes later. How many seconds is this? 2. The United States is of course the world’s largest producer of beer. It makes a whopping 5 billion gallons each year. That is 5,000,000,000 gallons. Convert this quantity to liters, if there is 3.79 liters per gallon. 3. Did you know that the Earth has another moon? Cruithne, as it is called, takes 770 years to complete a horseshoe-shaped orbit around Earth, the scientists say, and it will remain in a suspended state around Earth for at least 5,000 years. Convert its orbit years into hours. 4. Baskin Robbins once made ketchup ice cream. This was the only vegetable flavored ice cream produced. However, they discontinued it since they thought it would not sell well. One scoop of ketchup ice cream weighed 250 grams. Convert this into pounds. There are 2.2 pounds per kilogram. 5. There are approximately 102,000 miles of blood vessels in the human body. Convert this into kilometers, if there are 1.61 kilometers per mile. 6. African Baobab tree's circumference can reach 180 feet. If the trunk were hollow, 20 people would be able to fit inside of it. How many meters is this, if there are 3.28 feet per meter? 7. In 1912, a wrestling match in Stockholm between Finn Alfred Asikainen and Russian Martin Klein lasted more than 11.0 hours. Klein eventually won, but was to0 tired to participate in the championship match. Convert this time into seconds. 8. In 1976, a Los Angeles secretary named Jannene Swift officially married a 50.0- pound rock. More than twenty people witnessed the ceremony. Convert this into grams, if there are 2.2 pounds per kilogram. 9. The smallest stamp in the world was issued in 1863 by the Columbian state of Bolivar and measured 9.5 mm across. Convert this into inches, if there are 2.54 cm per inch. 10. The most expensive perfume in the world is Parfum VI, which was made by Arthur Burnham. A 4-inch bottle that is covered with 24-carat gold costs $71,380. If the bottle contains 85.5 cm3 of gold, what is its mass in pounds? The density of gold is 19.3 grams per cm3. 11. The world's deepest gold mine is 7.0 kilometers below the surface of the Earth. How far is that in feet? 12. Chloroform used to be used as an anesthetic, but is now banned. What is the mass in kilograms of 355 ml of chloroform if 1 ml of chloroform weighs 1.49 grams? 13. 27-year old heir to a sausage empire was handed a ticket for 174,000 dollars for driving at 80 km/hr in a 40-km/hr zone. This is because the speeding tickets in Finland are based on how much money a person makes. Convert 80 km/hr into miles per hour. 14. Suppose the European automobile described above gets 25.0 miles to the gallon. What would this be in kilometers per liter? 15. The world’s largest hot dog ever made was a whopping 6.90 meters long and 115 kg heavy. Convert this into lbs per foot. A GREAT PRACTICE SHEET!

A. Convert:

500 mL = ______L .068 Kg = ______cg 5 Mbytes = ______bytes

4.8 x 1012 ps = ______ds 7.3 L = ______dL 5.2 x 10-4 mm = ______nm

B. Circle the larger measurement of the two.

2.5 Kg or 2300 mg 45 m or .23 mm 1.5 x 103 cal or .85 kcal

C. Tell how many significant figures are in each of the following:

4.2030 _____ .0065 _____ 3.07 x 106 _____ 5300 _____ 8760 _____ 50550 _____ .000440 _____ 2.2200 _____ 80600 _____ .002002 _____

D. Rewrite the following numbers so they each have 3 significant figures.

5.34029 ______.00128906 ______256.0 ______

607809 ______6.325 x 1012 ______210.288 ______

E. Rewrite in scientific notation ( keep the same number of sig figs!)

.0018 ______245.0 ______12.8 x 109 ______

6400000 ______.000070 ______5610 x 103 ______

F. Perform the indicated problems. Remember sig figs, and show your work!

31.001 + 16.42 + 1.2 = ______

.006 + 3.07 + 4.21 = ______

5.30 x 6.21 x 20 = ______

(5.3 x 102 ) ( 1.68 x 103 ) (2.3 x 10-3 ) = ______

61.1 - 34.06 + 1.288 = ______

(3.56 x 10-3) ( 5.02 x 108 ) = ______

( 4.2 x 106) ( 1.7 x 10-2) = ______

If the density of lead is 11.3 g/cm3, what is the mass of a bar 3.0 cm x 4.0 cm x 10 cm? A silver liquid is found to weigh 2.52 x 104 g and have a volume of 3426 mL. Is this likely to be mercury? ( The density of mercury is 13.6 g/mL) An irregularly shaped piece of metal was dropped into a graduated cylinder of water measuring 11.40 mL. The water level rose to 16.80 mL. The mass of the metal was 61.05 g. What is the density of the metal? Is the metal lead? Calculate the density of a lead block that has a mass of 20 grams and a volume of .98 cm3. Calculate the density of an iron hammer that has a mass of 16 grams and a volume of 2 mL. What volume in liters does a pool of water have that has a density of 1.0 grams/milliliter and a mass of 24,300 kilograms? What mass does a room of air have if the density of air is .0013 grams/cm3 and the volume of the room is 10,000 cm3? How many atoms are contained within 13.2 cm3 of aluminum? The density of aluminum is 2.7 g/cm3. (Hint - 27 grams of aluminum contain 6.02 x 1023 atoms!)

ANOTHER GREAT PRACTICE SHEET!

Perform the following calculations rounding off to the correct number of significant digits.

______1. 8.54 + 143.1

______2. (.940 x 9700) x 8243

______3 . 500 (112.5 - 8.783)

______4. 54 x 487

______5. .00035 x 44.9

Do the following problems. Show your work. Remember significant digits.

6. Convert 300.0 mm/s to km/hr.

7. A cylindrical object has a diameter of 3.0 cm a mass of 400.0 grams and is 15.0 cm high What is its density in kg/m3? Volume of cylinder = π r2h

8. Convert 25.0 mg of Pb to cubic meters. The density of Pb is 11.3 g/cc.

9. Convert 50.0 kg/L to µg/kL

10. Convert 45 g/l to mg/m3

Indicate the correct number of significant digits in the following numbers.

11. .00044 12. 89.000 13. 5055 14. 876000 15. 362.220 16. 362.220

Perform the following calculations, keeping track of significant figures AND units!

17. 23.45 g + .2300 g + 12000g + .00345 g = 18. 34.7 mL - 2088 mL - 456.003 mL - 130,000 mL = 19. 45.667 m x 23.3m x 12.00m x 2000m = 20. (.00093 g/.3800g) / (140.0g / .000004g) = 21. (13.22 cm x 20.0 cm) / (34500 cm x .000013 cm) = 22. (13.66 L2 + 22.4 L2)/(23000L x .00462L) = 23. (14.6 g - 16.996g) + (7.0023 g x 230,000) = 24. (13.667 mL2 + 20.0 mL2 + 3400 mL2) / 4.0mL = 25. (20300 m x 14.67 m x .0003 m) / 10000 m = 26. (23.004 mm x 103 mm x 400 mm) - (16.4 mm3) =

Determine the number of significant figures in each of the following numbers. Then, indicate what two numbers it falls between on the measuring device being used!

(a) 24.5 grams (b) 540 liters (c) .52 centimeters (d) 98.4 kilograms (e) 15,000 milligrams (f) 566.0 mm (g) 3,400 meters (h) 2,000 megagrams (i) 2452 nanoliters (j) 23.58 km (k) 70 grams (l) 44 ml (m) 15,000 liters (n) 190.05 ml (o) 5.7 grams (p) 443 mL (q) 100.1 g (r) 640,002 m (r) 473 ml (s) 20.020 g (t) 0.002 meter (u) 1,000,000 liters (v) 4,200 km (w) .0020 g (x) 0.10 liter (y) 1.0004230 g (z) 104.20 g

SCIENTIFIC NOTATION PROBLEMS!

Convert to scientific notation:

1. 67,001 2. 54.65 3. .00453 4. 123.4 5. .0992 6. 4,009,001 7. .0078500 8. 890.00

Do the following calculations – if applicable, make sure to keep track of units as well!

9. 1.02 x 109 m + 3.45 x 107 m = 10. 4.87 x 10-3 cm - 1.03 x 10-5 cm = 11. 1.99 x 1011 mL + 6.82 x 109 mL = 12. 4.22 x 1023 atoms / 1.22 x 1019 atoms = 13. 3.90 x 10-11 grams2 / 1.22 x 106 grams = 14. 4.22 x 104 cL x 1.22 x 105 cL = 15. (2.33 x 10-4 m - 1.95 x 103 m)(7.00 x 102 m + 4.32 x 10-1 m) = 16. (1.366 x 103 g)( 2.44 x 10-8 g) + (3.11 x 1011 g3/1.22 x 1010 g) = 17. (9.90 x 10-9 s3)/(5.56 x 10-13 s) - (1.22 x 10-11 s)(4.32 x 10-10 s) = 18. (7.40 x 1025 mg)(1.22 x 10-23 mg) + (1.22 x 10-10 mg)(4.90 x 10-11 mg) = 19. (3.44 x 105) x (1.24 x 109) = 20. (6.23 x 102) x (2.03 x 108) = 21. (7.88 x 1010)/(3.22 x 104) = 22. (2.44 x 10-4) x (6.02 x 104) = 23. (3.02 x 10-3)/(5.78 x 10-6) = 24. (2.44 x 10-4) x (6.70 x 10-6)/(7.02 x 10-4) = 25. (1.240 x 103) + (3.45 x 101) = 26. (4.56 x 10-2) + (9.02 x 10-1) = 27. (6.00 x 10-4) – (7.33 x 10-6) = 28. (7.50 x 1011) + (4.02 x 108) = 29. (9.02 x 10-4) + (1.56 x 106) = 30. (2.02 x 102) + (6.78 x 104) = 31. (1.50 x 1013) – (9.97 x 10-4) = 32. (3.77 x 103) + (2.44 x 105) x (4.22 x 10-3) = TRICKY METRIC CONVERSIONS!

2300 cm3 to m3 3.66 x 10-3 Km to pm

550 mL to dm3 9.0 x 10-15 GL to L

300 ft3 to m3 1.22 x 10-11 Mm to m

25.0 in3 to cm3 2.11 x 1015 nm to Mm

.95 miles3 to L 7.89 x 10-8 Gg to mg

43.3 m3 to dm3 1.01 x 1014 mg to Dg

67990 cm3 to Dm3 4.50 x 105 cg to Hg

35,600 mL to m3 3.45 x 1023 pL to ML

90,000 cm3 to in3 2.33 x 1018 nL to GL

2345 m3 to ft3 39,884 cm3 to Mm3

5.30 x 10-6 Dm3 to dL 2.2 x 10-13 KL to Hm3

2.80 x 108 nL to Km3 1.22 x 105 Hg to cg ULTIMATE MATHEMATICS WORKSHEET

Always remember – keep track of significant figures!

1. The land area of Greenland is 840,000 mi2, with only 132,000 mi2 free of perpetual ice. The average thickness of this ice is 5000 ft. Estimate the mass of the ice in grams. The density of ice is 0.917 g/cm3.

2. A gas at 250C exactly fills a container previously determined to have a volume of 1.05 x 103 cm3. The container plus gas are weighed and found to have a mass of 837.6 g. The container, when emptied of all gas, has a mass of 836.20 g. What is the density of the gas in kg/L?

3. When 10.0 g of marble chips (calcium carbonate) are treated with 50.0 mL of hydrochloric acid (density 1.096 g/mL), the marble dissolves, giving a solution and releasing carbon dioxide gas. The solution weighs 60.4 g. How many liters of carbon dioxide gas are released? The density of the gas is 1.798 g/L.

4. Calculate the mass of 65 cm3 of mercury in grams, given that it has a density of .0136 kg/mL.

5. Do the following conversions:

a. 136.2 cm = ______nm b. 5002 mL = ______m3 c. .0032 Mg = ______Dg d. 45,000 pm = ______m e. 5.0 x 10-9m = ______pm f. 3.5 x 10-2mL = ______nL

6. Do the following calculations:

a. (55.01 + 2300) x (103 – 2.4) = b. (12,000 x .4520)/(34.226 x .002300) = c. (3.00 x 10-12)(1.2 x 1023)/(4.390 x 109)(1.0202 x 10-7) = d. (200 + 51.230)/(34.512 + 220) = e. (9.0400 x 4001)/(32.6 x 1.2 x 10-8) = f. (160 + 2.00) – (.0400 x 45.00) =

7. A copper refinery produces a copper brick weighing 150 lbs. If the copper is drawn into wire whose diameter is 8.25 mm, how many feet of copper can be obtained from the brick? The density of copper is 8.94 g/cm3. (2.2 lbs = 1.00 kg, 2.54 cm = 1.00 inch, 12.00 inches = 1.00 ft)

8. The average price for a gallon of gasoline in the U.S. is $1.55/gallon. What would the price of gasoline be in Europe, where they charge you per liter? (1.00 L = 1.057 quarts, and 1.00 gallons = 4.00 quarts)

9. An individual suffering from high cholesterol levels in her blood has 285 mg of cholesterol per 100.0 mL of blood. If the total blood volume of the individual is 5.30 L, how many grams of total blood cholesterol does the individual contain? 10. The recommended adult dose of Elixophyllin, a drug used to treat asthma, is 6.00 mg/kg of body mass. Calculate the dose in mg for a 150 lb person. (2.2 lbs = 1.00 kg)

11. A sample of an ethanol-water solution has a volume of .0542 dm3 and a mass of 4.96 x 107 ug. What is the percentage of ethanol (by mass) in the solution? (Assume there is no change in volume when the pure compounds are mixed). The density of ethanol is .789 g/cm3 and that of water is 0.998 g/cm3. Alcoholic beverages are rated in proof, which is a measure of the relative amount of ethanol in the beverage. Pure alcohol is 200 proof; a solution that is 50% ethanol by mass is exactly 100 proof. What is the proof of the given ethanol-water solution? Significant figures are not necessary for the proof! Round the nearest whole number for the proof!

12. A steel sphere has a radius of 1.58 inches. If this steel has a density of 7.88 g/ ml, what is the mass of the sphere in hectograms?

13. You have a piece of gold jewelry weighing 93.5 decigrams. Its volume is .0654 cL. Assume that the metal is an alloy (mixture) of gold and silver, which have densities of 19.3 g/cm3 and 10.5g/cm3, respectively. Also assume that there is no change in volume when the pure metals are mixed. Calculate the percentage of gold, by mass, in the alloy. The relative amount of gold in an alloy is measured in karats. Pure gold is 24 karats; an alloy of 50% gold is 12 karats. State the proportion of gold in the jewelry in karats. Significant figures are not necessary for the karat measurement! Round the nearest whole number for the karat measurement!

14. What is the density of the Ca2+ ion? The radius of the Ca2+ ion is 1.14 Angstroms and its mass is 40.078 atomic mass units. Give your answer in g/m3. Be sure to enter your answer to the proper number of significant figures.

15. What is the density of the Pb+2 ion? The radius of the Pb+2 ion is 1.43 Angstroms and its mass is 207.2 atomic mass units. Give your answer in g/m3. Be sure to enter your answer to the proper number of significant figures.

16. Given that a Newton is equal to a quarter pound, that an inch is 2.54 cm, and that a Pascal is a Newton per square meter, express a pressure of 30.0 pounds per square inch (psi) in KiloPascals.

17. HCN is a poisonous gas, used to commit murders. It is produced by the reaction of sodium cyanide powder and sulfuric acid. The lethal dose is 300.0 mg HCN per kilogram of air when inhaled. What amount of HCN in mg could give a lethal dose in a room that is 12 foot by 15 foot by 8.0 foot, if the density of air is .00118 g/cm3?

18. A student gently drops an object weighing 4.55 x 10-4 Mg into an open vessel that is full of acetone, so that a volume of acetone spills out equal to the volume of the object. The experimenter now finds that the vessel and its contents weigh only 438 grams more than the vessel full of acetone alone. The density of acetone is 0.790 g/cm3. What is the density of the object, in grams per mL? What is the identity of the object, assuming it is made of an element?