Measurement: Changing Metric Units

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MAIN IDEA Change metric units of length, capacity, and mass. New Vocabulary metric system meter liter gram kilogram Math Online glencoe.com " Extra Examples " Personal Tutor " Self-Check Quiz 6-5 Measurement: Changing Metric Units The lengths of two objects are shown below. Object Length (millimeters) Length (centimeters) paper clip454.5 CD case14414.4 1.

Select three other objects. Find and record the width of all five objects to the nearest millimeter and tenth of a centimeter. 2.

Compare the measurements of the objects, and write a rule that describes how to convert from millimeters to centimeters. 3. Measure the length of your classroom in meters.

Make a conjecture about how to convert this measure to centimeters. Explain. The metric system is a decimal system of measures.

The prefixes commonly used in this system are kilo-, centi-, and milli-. Prefix Meaning In Words Meaning In Numbers kilo-thousands1,000 centi-hundredths 0.01 milli-thousandths 0.001 In the metric system, the base unit of length is the meter (m). Using the prefixes, the names of other units of length are formed.

Notice that the prefixes tell you how the units relate to the meter. UnitSymbolRelationship to Meter kilometerkm1 km = 1,000 m1 m = 0.001 km meterm1 m = 1 m centimetercm1 ... more. less.

cm = 0.01 m1 m = 100 cm millimetermm1 mm = 0.001 m1 m = 1,000 mm The liter (L) is the base unit of capacity , the amount of dry or liquid material an object can hold. The gram (g) measures mass , the amount of matter in an object. The prefixes can also be applied to these units. Whereas the meter and liter are the base units of length and capacity, the base unit of mass is the kilogram (kg). 304 Chapter 6 Ratios and Proportions 0304_0309_CH06_L5_874046.indd 304 9/21/07 7:19:07 PM Real-World Link The maximum weight of a grizzly bear is 521.64 kilograms. Source: North American Bear Center To change a metric measure of length, mass, or capacity from one unit to another, you can use the relationship between the two units and multiplication by a power of 10. Convert Units in the Metric System 1 Convert 4.5 liters to milliliters. You need to convert liters to milliliters. Use the relationship 1 L = 1,000 mL. 1 L = 1,000 mL Write the relationship. 4.5 × 1 L = 4.5 × 1,000 mL Multiply each side by 4.5 since you have 4.5 L. 4.5 L = 4,500 mL To multiply 4.5 by 1,000, move the decimal point 3 places to the right. 2 Convert 500 millimeters to meters. You need to convert millimeters to meters. Use the relationship 1 mm = 0.001 m. 1 mm = 0.001 m Write the relationship. 500 × 1 mm = 500 × 0.001 m Multiply each side by 500 since you have 500 mm. 500 mm = 0.5 m To multiply 500 by 0.001, move the decimal point 3 places to the left. Complete. a. 25.4 g = kg b. 158 mm = m 3 BEARS The California Grizzly Bear was designated the official state animal in 1953. Use the information at the left to find the maximum weight of a grizzly bear in grams. You are converting kilograms to grams. Since the maximum weight of a grizzly bear is 521.64 kilograms, use the relationship 1 kg = 1,000 g. 1 kg = 1,000 g Write the relationship. 521.64 × 1 kg = 521.64 × 1,000 g Multiply each side by 521.64 since you have 521.64 kg. 521.64 kg = 521,640 g To multiply 521.64 by 1,000, move the decimal point 3 places to the right. So, the maximum weight of a grizzly bear is 521,640 grams. c. FOOD A bottle contains 1.75 liters of juice. How many milliliters is this? Metric Conversions When converting from a larger unit to a smaller unit, the power of ten being multiplied will be greater than 1. When converting from a smaller unit to a larger unit, the power of ten will be less than 1. Lesson 6-5 Measurement: Changing Metric Units 305 0304_0309_CH06_L5_874046.indd 305 9/21/07 7:19:10 PM KeyConcept Customary and Metric Relationships Type of Measure Customary Metric Length 1 inch (in.) H 2.54 centimeters (cm) 1 foot (ft) H 0.30 meter (m) 1 yard (yd) H 0.91 meter (m) 1 mile (mi) H 1.61 kilometers (km) Weight/Mass 1 pound (lb) H 453.6 grams (g) 1 pound (lb) H 0.4536 kilogram (kg) 1 ton (T) H 907.2 kilograms (kg) Capacity 1 cup (c) H 236.59 milliliters (mL) 1 pint (pt) H 473.18 milliliters (mL) 1 quart (qt) H 946.35 milliliters (mL) 1 gallon (gal) H 3.79 liters (L) To convert measures between customary units and metric units, use the relationships below. Convert Between Measurement Systems 4 Convert 17.22 inches to centimeters. Round to the nearest hundredth if necessary. Use the relationship 1 inch H 2.54 centimeters. 1 inch H 2.54 cm Write the relationship. 17.22 × 1 in. H 17.22 × 2.54 cm Multiply each side by 17.22 since you have 17.22 in. 17.22 in. H 43.7388 cm Simplify. So, 17.22 inches is approximately 43.74 centimeters. 5 Convert 828.5 milliliters to cups. Round to the nearest hundredth if necessary. Since 1 cup H 236.59 milliliters, multiply by 1 c _ 236.59 mL . 828.5 mL H 828.5 mL · 1 c _ 236.59 mL Multiply by 1 c _ 236.59 mL . H 828.5 c _ 236.59 or 3.5 c Simplify. So, 828.5 milliliters is approximately 3.5 cups. Complete. Round to the nearest hundredth if necessary. d. 7.44 c H mL e. 22.09 lb H kg f. 35.85 L H gal Alternative Method When converting 17.22 inches to centimeters, you can use the relationship 1 in. H 2.54 cm or the unit ratio 2.54 cm _ 1 in. . 306 Chapter 6 Ratios and Proportions 0304_0309_CH06_L5_874046.indd 306 9/21/07 7:19:12 PM Real-World Link Before the seventeenth century, people thought light was transmitted instantly. Now, we know that light is too fast for the delay to be noticeable. Source: University of California, Riverside Convert with Rates 6 LIGHT The speed of light is about 186,000 miles per second. Find the approximate speed of light in kilometers per second. Since 1 mile H 1.61 kilometers, multiply by 1.61 km _ 1 mi . 186,000 mi _ s H 186,000 mi _ 1 s × 1.61 km _ 1 mi Multiply by 1.61 km _ 1 mi . H 299,460 km _ 1 s Simplify. So, the speed of light is approximately 299,460 kilometers per second. g. RUNNING Chuck runs at a speed of 3 meters per second. About how many feet per second does Chuck run? Examples 1, 2, 4, 5 (pp. 305 3306) Complete. Round to the nearest hundredth if necessary. 1. 3.7 m = cm 2. 550 m = km 3. 1,460 mg = g 4. 2.34 kL = L 5. 9.36 yd H m 6. 11.07 pt H mL 7. 58.14 kg H lb 8. 38.44 cm H in. Examples 3, 6 (pp. 305, 307) 9. SPORTS About how many feet does a team of athletes run in a 1,600-meter relay race? Complete. Round to the nearest hundredth if necessary. 10. 720 cm = m 11. 983 mm = m 12. 3.2 m = cm 13. 0.03 g = mg 14. 997 g = kg 15. 82.1 g = kg 16. 9.1 L = mL 17. 130.5 kL = L 18. 3.75 c H mL 19. 41.8 in. H cm 20. 156.25 lb H kg 21. 9.5 gal H L 22. 680.4 g H lb 23. 4.725 m H ft 24. WATERFALLS At 979 meters tall, Angel Falls in Venezuela is the highest waterfall in the world. How many kilometers tall is the waterfall? 25. FOOD An 18-ounce jar contains 510 grams of grape jelly. How many kilograms of grape jelly does the jar contain? For Exercises 10 323 24 327 See Examples 1, 2, 4, 5 3, 6 HOMEWORK HELP HELP For Exercises 10 323 24 327 See Examples 1, 2, 4, 5 3, 6 HOMEWORK HELP HELP Lesson 6-5 Measurement: Changing Metric Units 307 0304_0309_CH06_L5_874046.indd 307 9/21/07 7:19:13 PM See pages 683, 709. EXTRA PRACTICE PRACTICE Real-World Link The Mackinac Bridge opened on November 1, 1957. It is the longest two-tower suspension bridge between bases in the Western Hemisphere. Source: Encyclopaedia Britannica 26. CYCLING Ramon rides his bike at a rate of 8 kilometers per hour. About how many miles per hour can Ramon ride his bike? 27. BIRDS A gull can fly at a speed of 22 miles per hour. About how many meters per hour can a gull fly? Complete. Round to the nearest hundredth if necessary. 28. 8.18 qt H L 29. 15.09 km H yd 30. 72.26 cm H ft 31. 0.445 T H g Order each set of measures from least to greatest. 32. 0.02 km, 50 m, 3,000 cm 33. 660 mL, 0.06 L, 6.6 kL 34. 0.32 kg, 345 g, 35,100 mg 35. 2,650 mm, 130 cm, 5 m 36. ANALYZE TABLES The table shows the BridgeLength (m) Mackinac, MI1,158 George Washington, NY1,067 Tacoma Narrows II, WA853 Oakland Bay, CA704 Pennybacker, TX345 Sunshine Skyway, FL8,712 Golden Gate, CA2,780 lengths of bridges in the United States. Which bridges are about 1 kilometer in length? Justify your answer. 37. CARPENTRY Jacinta needs a 2.5-meter pole for a birdfeeder that she is building. How many centimeters will she need to cut off a 3-meter pole in order to use it for the birdfeeder? 38. BAKING A bakery uses 900 grams of peaches per cobbler. How many cobblers can be made using 10.5 pounds of peaches? H.O.T. Problems 39. FIND THE ERROR Jake and Gerardo are converting 3.25 kilograms to grams. Who is correct? Explain your reasoning. JakeGerardo 3.25 kg = 3,250 g 3.25 kg = 0.00325 g CHALLENGE For Exercises 40 342, use the following information. The metric prefix giga refers to something one billion times larger than the base unit. 40. How many meters are in one gigameter? 41. About how many miles are in one gigameter? Round to the nearest hundredth. 42. The distance from Earth to the Sun is approximately 93 million miles. About how many gigameters is this? Round to the nearest hundredth. 308 Chapter 6 Ratios and Proportions 0304_0309_CH06_L5_874046.indd 308 9/21/07 7:19:15 PM 44. The table shows the mass of four wireless telephones. Find the approximate total mass of the telephones in kilograms. Telephone OwnerMass (g) Elena100.4 Kevin70.8 Marissa95.6 Corey120.4 A 0.39 kilogram B 3.9 kilograms C 39.0 kilograms D 390.0 kilograms 45. Which relationship between the given units of measure is correct? F One gram is 1 _ 100 of a centigram. G One meter is 1 _ 100 of a centimeter. H One gram is 1 _ 1,000 of a kilogram. J One milliliter is 1 _ 100 of a liter. 46. MEASUREMENT A certain car weighs 3,200 pounds. What is the weight of the car in tons? (Lesson 6-4) 47. MEASUREMENT The table shows the number of inches per foot. Graph the data. Then find the slope of the line. Explain what slope represents. (Lesson 6-3) Feet ( x ) 1234 Inches ( y ) 12243648 Add or subtract. Write in simplest form. (Lesson 5-3) 48. 3 4 _ 7 + 1 1 _ 7 49. 8 3 _ 5 - 2 2 _ 5 50. 9 1 _ 6 + 4 3 _ 8 51. 11 7 _ 10 - 5 3 _ 4 52. BASKETBALL Jared made thirty-seven percent of his free-throw attempts during basketball practice. Write this percent as a decimal. (Lesson 4-7) PREREQUISITE SKILL Solve each equation. (Lesson 3-3) 53. 5 · 4 = x · 2 54. 9 · 24 = 27 · x 55. x · 15 = 12 · 4 56. 8 1 _ 2 · x = 11 · 17 43. MATH WR I T I N G IN Explain why it makes sense to multiply by a power of 10 that is greater than 1 when changing from a larger unit to a smaller unit. Lesson 6-5 Measurement: Changing Metric Units 309 0304_0309_CH06_L5_874046.indd 309 9/21/07 7:19:20 PM

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