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**1-3**Metric Measurements Warm Up Problem of the Day Lesson Presentation Course 2**Warm Up**Find each value. 1. 10 2. 10 3. 100 4. 100 2 4 100 10,000 3 2 10,000 1,000,000**Problem of the Day**Which is larger, 100 or 100 ? How do you know? 3 4 1004 is larger; the power of 100 is greater.**Additional Example 1: Choosing the Appropriate Metric Unit**Choose the most appropriate metric unit for each measurement. Justify your answer. A. The amount of water a runner drinks each day Liters—The amount of water a runner drinks each day is similar to the amount of water in a large water bottle. B. The length of a boat Meters—The length of a boat is similar to the length of several doorways. C. The mass of a car Kilograms—The mass of a car is similar to the mass of several hundred textbooks.**Check it Out: Example 1**Choose the most appropriate metric unit for each measurement. Justify your answer. A. The amount of liquid in 10 teardrops B. The mass of a pencil eraser C. The length of 15 soccer fields Milliliters—The amount of liquid in 10 teardrops is similar to the amount of liquid in several eyedroppers. Grams—The mass of a pencil eraser is similar to the mass of a few paperclips. Kilometers—The length of 15 soccer fields is similar to the length of 10 football fields.**The prefixes of metric units correlate to place values in**the base-10 number system. The table shows how metric units are based on powers of 10. You can convert units within the metric system by multiplying or dividing powers of 10. To convert to a smaller unit, you must multiply. To convert to a larger unit, you must divide.**Additional Example 2A: Converting Metric Units**Convert the measure. 530 cL to liters 100 cL = 1L, so divide by 100. 530 cL = (530 ÷ 100) L Move the decimal point 2 places left: 530. = 5.3 L**Additional Example 2B: Converting Metric Units**Convert the measure. 1,070 g to milligrams 1 g = 1000 mg, so multiply by 1000. 1,070 g = (1070 1000) mg Move the decimal point 3 places right: 1,070,000. = 1,070,000 mg**Check It Out: Example 2A**Convert the measure. 980 dm to meters 10 dm = 1m, so divide by 10. 980 dm = (980 ÷ 10) m Move the decimal point 1 places left: 980. = 98 m**Check It Out: Example 2B**Convert the measure. 580 g to centigrams 1 g = 100 cg, so multiply by 100. 580 g = (580 100) cg Move the decimal point 2 places right: 58,000. = 58,000 cg**Additional Example 3: Using Unit Conversions t**to Make ComparisonsElizabeth purchases one pumpkin that weighs 3 kg and another that weighs 2,150 g. Which pumpkin weighs more? Use estimation to explain why your answer makes sense. You can convert the mass of Elizabeth’s pumpkin to grams. 1 kg = 1000 g, so multiply by 1,000. 3 kg = (3 1,000) g Move the decimal point 3 places right: 3.000. = 3,000 g 2,150 g is about 2 kg. Since 2 kg < 3 kg, Elizabeth’s 3 kg pumpkin weighs more.**Check It Out: Additional Example 3**Tyesha purchases a bag of potatoes that weighs 2.5 kg and another bag that weighs 3,850 g. Which bag weighs more? Use estimation to explain why your answer makes sense. You can convert the mass of Tyesha’s bag to grams. 1 kg = 1000 g, so multiply by 1,000. 2.5 kg = (2.5 x 1,000) g Move the decimal point 3 places right: 2.500. = 2,500 g 3,850 g is about 4 kg. Since 4 kg > 2.5 kg, Tyesha’s 3,850 g bag weighs more.**Lesson Quiz**Convert each measure. 1. 1,270 g to kilograms 2. 890 cm to millimeters 3. 750 mL to liter 4. 122 km to meters 5. 800 mg to grams 1.27 kg 8,900 mm 0.75 L 122,000 m 0.8 g 6. Rosa walks 1.5 km to the library. Meghan walks 2,200 m to the library. Who walks farther? Use estimation to explain why your answer makes sense. Meghan walks farther. 2,200 m = 2.2 km**1-4**Applying Exponents Course 2 Warm Up Problem of the Day Lesson Presentation**Warm Up**Find each value. 1.92 3. 152 5. 103 81 2. 122 144 225 4. 102 100 1,000 10,000 6. 104**Problem of the Day**Each day, Lowell runs one more lap than he did the day before. After seven days he has run a total of 77 laps. How many laps did he run on the first day? 8**Vocabulary**scientific notation**The distance from Venus to the Sun is over 100,000,000**kilometers. You can write this number as a power of ten by using a base of ten and an exponent. 10 · 10 · 10 · 10 · 10 · 10 · 10 · 10 = 108 Power of ten**The table shows several powers of ten.**Power of 10 Meaning Value 101 10 10 102 10 · 10 100 10 · 10 · 10 1,000 103 104 10 · 10 · 10 · 10 10,000**Additional Example 1A: Multiplying by Powers of Ten**Multiply 14 · 103. Method 1: Evaluate the power. Multiply 10 by itself 3 times. 14 · 103 = 14 · (10 · 10 · 10) Multiply. = 14 · 1,000 = 14,000**Additional Example 1B: Multiplying by Powers of Ten**Multiply 14 · 103. Method 2: Use mental math. Move the decimal point 3 places. (You will need to add 3 zeros.) 14 · 103 = 14.000 3 places = 14,000**Check It Out: Example 1A**Multiply 12 · 102. Method 1: Evaluate the power. Multiply 10 by itself 2 times. 12 · 102 = 12 · (10 · 10) Multiply. = 12 · 100 = 1,200**Check It Out: Example 1B**Multiply 12 · 102. Method 2: Use mental math. Move the decimal point 2 places. (You will need to add 2 zeros.) 12 · 102 = 12.00 2 places = 1,200**Scientific notation is a kind of shorthand that can be used**to write large numbers. Numbers expressed in scientific notation are written as the product of two factors. In scientific notation, 17,900,000 is written as 7 1.79 x 10 A power of 10 A number greater than or equal to 1 but less than 10**Writing Math**In scientific notation, it is customary to use a multiplication cross () instead of a dot.**6 places**Additional Example 2: Writing Numbers in Scientific Notation Write the number 4,340,000 in scientific notation. Move the decimal point to get a number that is greater than or equal to 1 and less than 10. 4,340,000 = 4,340,000 The exponent is equal to the number of places the decimal point is moved. = 4.34 106**6 places**Check It Out: Example 2 Write the number 8,421,000 in scientific notation. Move the decimal point to get a number that is greater than or equal to 1 and less than 10. 8,421,000 = 8,421,000 The exponent is equal to the number of places the decimal point is moved. = 8.421 106**Additional Example 3: Writing Numbers in Standard Form**The population of China in the year 2000 was estimated to be about 1.262 109. Write this number in standard form. Since the exponent is 9, move the decimal point 9 places to the right. 1.262 109 = 1.262000000 = 1,262,000,000 The population of China was about 1,262,000,000 people.**Check It Out: Example 3**The distance from the Earth to the Sun is calculated to be 1.5 108 kilometers. Write this distance in standard form. Since the exponent is 8, move the decimal point 8 places to the right. 1.5 108 = 1.50000000 = 150,000,000 The distance from the Earth to the Sun is about 150,000,000 kilometers.**Mexico: 1.06 108 Brazil: 1.86 108**Notice that 1.06 < 1.86. So 1.06 108 < 1.86 108 Additional Example 4: Comparing Numbers in Scientific Notation In 2005, the population of Mexico was 1.06 108 and the population of Brazil was 1.86 108. In which country do more people live? To compare numbers written in scientific notation, first compare the exponents. If the exponents are equal, then compare the decimal portion of the numbers. Brazil has more people living there.**Ty’s jar: 0.76 104 Laurel’s jar: .93 103**Notice that 4 > 3. So .76 104 > .93 103 Check It Out: Additional Example 4 The number of coins in Ty’s jar was 0.76 104 and number of coins in Laurel’s jar was 0.93 103. In which jar are there more coins? To compare numbers written in scientific notation, first compare the exponents. If the exponents are equal, then compare the decimal portion of the numbers. Ty’s jar has more coins in it.**Lesson Quiz: Part I**Multiply. 2,500 1. 25 102 2. 18 104 180,000 3. 110 102 11,000 4. 3.742 103 3,742**Lesson Quiz: Part II**Write each number in scientific notation. 5. 7,400,000 6. 45,000 7. Earth is about 9.292 107 miles from the Sun. Write this number in standard form. 7.4 106 4.5 104 92,920,000