HFCC Math Lab General Math Topics - Metric System: Shortcut Conversions of Units within the Metric System In this handout, we will work with three basic units of measure in the metric system: meter: gram: liter: The meter is a measure of distance. The meter is used in the same way as feet and yards are used to measure distance. A meter is slightly longer than one yard. The abbreviation for meter is m. The gram is a measure of mass or weight. The gram is used in the same way as ounces and pounds are used to measure weight. A gram is about the weight of one raisin. The abbreviation for gram is g. The liter is a measure of capacity. The liter is used in the same way as pints, quarts and gallons are used to measure capacity. A liter is slightly larger than one quart. The abbreviation for liter is L. Used with a prefix, the abbreviation for liter is l. Metric measurement is based on the decimal system. This means that its units are related by powers of ten. Each prefix in the metric system has the same meaning, no matter which basic metric unit it precedes. For example if given a kilometer, a kilogram or a kiloliter, the prefix kilo means 000 times. Therefore: kilometer = 000 meters kilogram = 000 grams kiloliter = 000 liters The metric prefixes that we will use in this handout, along with their symbols and meanings are listed in the chart below. Prefix Symbol Meaning Exs: km = 000 m kg = 000 g kilo k 000 times hg = 00 g hl = 00 L hecto h 00 times deka da 0 times deci d 0 of centi c 00 of milli m 000 of dm = m 0 cg = g 00 mg = g 000 dl = L 0 mm = m 000 ml = L 000 Revised 6/0
Note: When we multiply a number by 000, 00, 0,,, or, 0 00 000 moving the decimal point to the right or to the left. For example: all we are doing is 5.82 0 5. 8.2 58.2 5.82 000 5. 8 2 0. 5,820. 5,820 5.82. 5.82.582 0 5.82.0 5.82 0.0582 000 We can use the chart below to convert from one metric unit to another. The units in the table are listed from largest (km) to smallest (mm). When converting from one unit to another, find the given unit in the chart below. If the desired unit is located to the right or left, move the decimal point in the given number to the right or left as many spaces as is necessary to jump into that desired unit. Unit kilometer hectometer dekameter meter decimeter centimeter millimeter Abbreviation km hm dam m dm cm mm Relationship to a meter 000 meters 00 meters 0 meters meter 0 meter 00 meter 000 meter Examples: Fill in the blanks using the above chart...7 dam = cm Looking at the chart, we must jump three places to the right to move from dam to cm. Therefore, we move the decimal point in.7 three places to the right..7 dam.7 0 0. cm,700 cm 2. 5.6 mm = m Looking at the chart, we must jump three places to the left to move from mm to m. Therefore, we move the decimal point in 5.6 three places to the left. 5.6 mm = 0. 005.6 m = 0.0056 m. Revised 6/0 2
. 79 dm = km Looking at the chart, we must jump four places to the left to move from dm to km. Therefore, we move the decimal point in 79 four places to the left. Remember in a whole number, the decimal point is understood to be at the right of the number. So 79 79. 79 dm = 0. 0079. km = 0.0079 km An analogous chart can also be used when converting units in which the gram or liter is the basic unit of measurement. Using gram as the basic unit, we have: Unit kilogram hectogram dekagram gram decigram centigram milligram Abbreviation kg hg dag g dg cg mg Relationship to a gram 000 grams 00 grams 0 grams gram 0 gram 00 gram 000 gram Examples: Fill in the blanks using the above chart. 4..4 g = cg Looking at the chart, we must jump two places to the right to move from g to cg. Therefore, we move the decimal point in.4 two places to the right..4 g =. 40. cg = 40. cg 40 cg 5. 80. cg = kg Looking at the chart, we must jump five places to the left to move from cg to kg. Therefore, we move the decimal point in 80. five places to the left. 80. cg 0.0 0 0 8 0. kg 0.00080 kg Using liter as the basic unit, we have: Unit kiloliter hectoliter dekaliter liter deciliter centiliter milliliter Abbreviation kl hl dal L dl cl ml Relationship to a liter 000 liters 00 liters 0 liters liter 0 liter 00 liter 000 liter Revised 6/0
Examples: Fill in the blanks using the above chart. 6. 0.07 ml = kl Looking at the chart, we must jump six places to the left to move from ml to kl. Therefore, we move the decimal point in 0.07 six places to the left. 0.07 ml = 0. 000000.07 kl = 0.00000007 kl Another commonly used metric unit is the cubic centimeter abbreviated cm. cubic centimeter = milliliter That is, cm ml 7. 28,000 cm = L Since cm ml, the problem is equivalent to 28,000 ml = L Looking at the chart, we must jump three places to the left to move from ml to L. Therefore, we move the decimal point in 28,000 three places to the left. 28,000 ml = 28. 000. L = 28.000 L = 28 L Thus 28,000 cm = 28 L 8. 4.2 L = cm Since cm ml, we must first change 4.2 L to ml. Looking at the chart, we must jump three places to the right to move from L to ml. Therefore, we move the decimal point in 4.2 three places to the right. 4.2 L = 4. 20. ml = 4,20 ml = 4,20 cm Thus 4.2 L 4,20 cm Revised 6/0 4
Exercises: Fill in the blanks using the charts in this handout.. 0.047 g = mg 2. 6 mm = cm 2. 0.02 kg = g. 20. cm = km. 5 dm = hm 4. 278 cm = L ml cm ) 4. 0.072 dam = km 5. 59. ml = cm 5. 2.8 hl = L 6. 700 ml cm ) cm = L ml cm ) 6. 0.6 L = ml 7. 2.8 L = cm ml cm ) 7. 0.72 cl = hl 8. 0.0827 m = mm 8. 2. m = cm 9. 2.4 mm = km 9. 0.42 g = kg 20. 5.7 ml = dal 0. 2 kg = mg 2. 5.2 dag = dg. 547 cg mg 22. 0.2 dm = dam Revised 6/0 5
Solutions to the odd-numbered exercises and answers to the even-numbered exercises:. 0.047 g = mg 2. 20 g Moving the decimal point three places to the right, we have 0.047 g = 4.7 mg. 5 dm = hm Moving the decimal point three places to the left, we have 5 dm = 0.05 hm 4. 0.00072 km 5. 2.8 hl = L 6. 600 ml Moving the decimal point two places to the right, we have 2.8 hl = 28 L 7. 0.72 cl = hl 8. 20 cm Moving the decimal point four places to the left, we have 0.72 cl = 0.000072 hl 9. 0.42 g = kg Moving the decimal point three places to the left, we have 0.42 g = 0.00042 kg 0. 2,000,000 mg. 547 cg = mg 2. 0.6 cm Moving the decimal point one place to the right, we have 547 cg = 5,470 mg. 20. cm = km Moving the decimal point five places to the left, we have 20. cm = 0.0020 km 4. 0.278 L 5. 59. ml = 6..7 L cm ; 59. ml = 59. cm since ml = cm Revised 6/0 6
7. 2.8 L = cm First we convert 2.8 L to ml. Moving the decimal point three places to the right, we have 2.8 L = 2,800 ml. Since ml = cm, 2.8 L = 2,800 ml = 2,800 cm 8. 82.7 mm 9. 2.4 mm = km Moving the decimal point six places to the left, we have 2.4 mm = 0.0000024 km 20. 0.00057 dal 2. 5.2 dag = dg Moving the decimal point two places to the right, we have 5.2 dag = 520 dg 22. 0.002 dam Revised 6/0 7