___________________________________ 8.1 Basic Terms & Conversions in the Metric System ___________________________________ Basic Units of Measurement: •Meter (m) used to measure length. A little longer than a yard. ___________________________________ ___________________________________ •Kilogram (kg) used to measure mass. A little more than 2 pounds. ___________________________________ •Liter (l) used to measure volume. A little more than a quart. •Celsius (°C) used to measure temperature. ___________________________________ ___________________________________ ch. 8 Angel & Porter (6th ed.) 1 The metric system is based on powers of 10 (the decimal system). ___________________________________ Prefix Symbol Meaning ___________________________________ kilo k 1000 x base unit ___________________________________ hecto h 100 x base unit deka da 10 x base unit ___________________________________ ——— ——— base unit deci d 1/10 x base unit ___________________________________ centi c 1/100 x base unit milli m 1/1000 x base unit ___________________________________ ___________________________________ ch. 8 Angel & Porter (6th ed.) 2 ___________________________________ Changing Units within the Metric System 1. To change from a smaller unit to a larger unit, move the ___________________________________ decimal point in the original quantity one place to the for each larger unit of measurement until you obtain the desired unit of measurement. ___________________________________ 2. To change form a larger unit to a smaller unit, move the decimal point in the original quantity one place to the ___________________________________ for each smaller unit of measurement until you obtain the desired unit of measurement. ___________________________________ khda—dcm ___________________________________ (larger) (smaller) ___________________________________ ch. 8 Angel & Porter (6th ed.) 3 ___________________________________ Example Convert the given unit to the unit indicated. #42 7 dam = ________ m ___________________________________ #46 1.34 ml = ________ l ___________________________________ #54 24 dm = ________ km ___________________________________ Example Arrange the quantities in order from smallest to largest. ___________________________________ #60 5.1 dam 0.47 km 590 cm ___________________________________ ___________________________________ ch. 8 Angel & Porter (6th ed.) 4 ___________________________________ 8.2 Length, Area, and Volume Length ___________________________________ Recall the meter is a little longer than a yard. It is used to measure things that we normally measure in feet or yards. ___________________________________ A kilometer is about 0.6 mile. It is used to measure things we normally measure in miles. ___________________________________ A centimeter is a little less than ½ inch.It is about the width of your little finger. A millimeter is about the thickness of a dime. ___________________________________ These are used to measure things we normally measure in inches. centimeters ___________________________________ 0123 4 5 6 789 10 inches ___________________________________ 0 1 234 ch. 8 Angel & Porter (6th ed.) 5 ___________________________________ Example Indicate the metric unit of measurement that you would use to express the following. ___________________________________ #26 The length of a jump rope ___________________________________ #28 The length of a paper clip ___________________________________ #32 The diameter of a jump rope ___________________________________ #36 The distance to the moon ___________________________________ ___________________________________ ch. 8 Angel & Porter (6th ed.) 6 Area ___________________________________ Used to measure two dimensional figures. The area of a figure is measured in ___________________________________ 1 m Area = (1 m)(1 m) = 1 m2 ___________________________________ 1 m ___________________________________ Square centimeters are used where we normally use square inches. Square meters replace square feet or square yards. ___________________________________ To measure large land areas, the metric system uses a square unit 100 meters on each side (a hectare). A hectare is about 2.5 acres. ___________________________________ Very large areas are measured in square kilometers. ___________________________________ ch. 8 Angel & Porter (6th ed.) 7 ___________________________________ Example Indicate the metric unit of measurement that you would use to express the following. ___________________________________ #62 The floor of your classroom ___________________________________ #66 Washington, D.C. ___________________________________ ___________________________________ A piece of notebook paper ___________________________________ ___________________________________ ch. 8 Angel & Porter (6th ed.) 8 ___________________________________ Volume Used to measure three dimensional figures. The volume of a figure ___________________________________ is measured in ___________________________________ 1 m Volume = (1 m)(1 m)(1 m) = 1 m3 ___________________________________ 1 m 1 m ___________________________________ Cubic meters are generally used to express the volume of large amounts of solid material. ___________________________________ ___________________________________ ch. 8 Angel & Porter (6th ed.) 9 ___________________________________ The volume of liquids is generally expressed in liters. A liter is a little larger than a quart. Liters are used in place of pints, quarts, and gallons. ___________________________________ Milliliters are used to express the volume of very small amounts of liquid. Kiloliters are used to express very large amounts of liquid. ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ch. 8 Angel & Porter (6th ed.) 10 ___________________________________ A liter is defined as the volume of a cubic decimeter. 1 liter = (1 dm)(1 dm)(1 dm) ___________________________________ Recall 1 dm = 10 cm, so 1 dm 1 liter = (10 cm)(10 cm)(10 cm) ___________________________________ 1 dm = 1000 cm3 [cm3 is sometimes 1 dm ___________________________________ abbreviated cc] ___________________________________ Also, since 1 l = 1000 ml, we have 1000 ml = 1000 cm3 ___________________________________ or 1ml = 1 cm3 ___________________________________ ch. 8 Angel & Porter (6th ed.) 11 In summary, ___________________________________ Volume in Volume in cubic units liters ___________________________________ 1 cm3 = 1 ml 1 dm3 = 1 l ___________________________________ 1 m3 = 1 kl ___________________________________ Example Indicate the metric unit of measurement that you would use to express the following. ___________________________________ #84 Water in a hot-water heater ___________________________________ #86 Air in a basketball ___________________________________ #90 Asphalt needed to pave a driveway ch. 8 Angel & Porter (6th ed.) 12 ___________________________________ Example #112 A rectangular fish tank is 70 cm long, 40 cm wide, and 20 cm high. ___________________________________ (a) How many cubic centimeters of water will the tank hold? (b) How many milliliters of water will the tank hold? ___________________________________ (c) How many liters of water will the tank hold? ___________________________________ ___________________________________ ___________________________________ ___________________________________ ch. 8 Angel & Porter (6th ed.) 13 ___________________________________ 8.3 Mass and Temperature Mass ___________________________________ Weight is a measure of the earth's gravitational pull. is the measure of the amount of matter (atoms and molecules) that ___________________________________ objects are made of. In space, the mass of an object does not change, but its weight does. On earth the mass of an object is ___________________________________ proportional to the weight of the object. For this course we can treat weight and mass as the same thing. ___________________________________ The kilogram is the basic unit of mass. It is a little more than 2 pounds. It is used to measure things we normally measure in pounds. ___________________________________ ___________________________________ ch. 8 Angel & Porter (6th ed.) 14 The gram is used to measure things we normally measure in ___________________________________ ounces. A large paper clip has the mass of about 1 g. ___________________________________ The milligram is used to measure extremely small quantities. It is used primarily in medical and scientific fields. ___________________________________ The metric tonne (t) is used to express the mass of heavy items. It is a little more than a ton (2000 pounds). ___________________________________ Example Indicate the metric unit of measurement that you would use to express the following. ___________________________________ #12 A box of cereal #14 A Cadillac ___________________________________ #16 A mosquito ___________________________________ ch. 8 Angel & Porter (6th ed.) 15 ___________________________________ In the metric system we have the following relationships: Volume in Volume Mass of ___________________________________ cubic units in liters water 1 cm3 = 1 ml = 1 g ___________________________________ 1 dm3 = 1 l = 1 kg ___________________________________ 1 m3 = 1 kl = 1 t (1000kg) ___________________________________ These relationships allow conversions between mass and volume. Try to convert your weight, in pounds, to gallons!