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Engage NY Module 1 Lesson 4 Objective: Use exponents to denote powers of 10 with application to metric conversions. Multiply and Divide Decimals by 10, 100, and 1000 Say the value as a decimal. Write the number and multiply it by 10. 32.4 x 10 = 324 Now show 32.4 divided by 10. 32.4 ÷ 10 = 3.24 Multiply and Divide Decimals by 10, 100, and 1000 Using your place value chart, show 32.4 x 100. 32.4 x 100 = 3240 Now show 32.4 ÷ 100. 32.4 ÷ 100 = 0.324 Multiply and Divide Decimals by 10, 100, and 1000 Using your place value chart, show 837 ÷ 1000. 837 Now ÷ 1000 = 0.837 show 0.418 x 1000. 0.418 x 1000 = 418 Write the Unit as a Decimal 9 tenths = _____ 10 tenths = ____ 20 tenths = ____ 30 tenths = ____ 70 tenths = ____ 9 hundredths = ____ 10 hundredths = ____ 11 hundredths = ____ 17 hundredths = ____ 57 hundredths = ____ 42 hundredths = ____ 9 thousandths = ____ 10 thousandths = ____ 20 thousandths = ____ 60 thousandths = ____ 64 thousandths = ____ 83 thousandths = ____ Write in Exponential Form 100 = 10? Write 100 in exponential form. 1,000 = 10? Write 1,000 in exponential form. 1,000 = 10³ 10,000 = 10? Write 10,000 in exponential form. 100 = 10² 10,000 = 10⁴ 1,000,000 = 10? Write 1,000,000 in exponential form. 1,000,000 = 10⁶ Converting Units 1 km = _____ m Fill in the missing number. 1 kg = _____ g Fill in the missing number. 1000 g 1 liter = ____ ml Fill in the missing number. 1000 m 1000 ml 1 m = _____ cm Fill in the missing number. 100 cm APPLICATION PROBLEM Mr. Brown wants to withdraw $1,000 from his bank and in ten dollar bills. How many ten dollar bills should he receive? Explain how you arrived at your answer. Concept Development – Problem 1 Draw a line 2 meters long. 0m 2m • With your partner, determine how many centimeters equal 2 meters. • 2 m = 200 cm • How is it that the same line can measure both 2 meters and 200 centimeters? • Discuss with a partner how we convert from 2 meters to 200 centimeters. • Multiply by 100 • Why didn’t the length of our line change? Discuss that with your partner. Concept Development – Problem 1 Draw a line 2 meters long. 0m 2m • With your partner, determine how many millimeters equal 2 meters. • 2 m = 2000 mm • How is it that the same line can measure both 2 meters and 2000 millimeters? • Discuss with a partner how we convert from 2 meters to 2000 millimeters. • Multiply by 1000 • Why didn’t the length of our line change? Discuss that with your partner. • Can we represent the conversion from meters to centimeters or meters to millimeters with exponents? Discuss this with your partner. Concept Development – Problem 1 • When we convert from centimeters to meters, we multiplied by 10², while to convert from meters to millimeters we multiplied by 10³. • However, if we convert from centimeters to meters we divide by 10² and to convert from millimeters to meters we divide by 10³. Concept Development – Problem 2 Draw a line 1 meter 37 centimeters long. 0m 0.5 m 1m 1 m 37 cm 1.5 m 2m • What fraction of a whole meter is 37 centimeters? • 37 hundredths • Write 1 and 37 hundredths as a decimal fraction. • 1.37 • With your partner, determine how many centimeters is equal to 1.37 meters both by looking at your meter strip and line and writing an equation using an exponent. • What is the equivalent measure in meters? • 137 centimeters • Show the conversion using an equation with an exponent. • 1.37 meters =1.37 x 10² = 137 centimeters • What is the conversion factor? • 10² or 100 Concept Development – Problem 2 • Convert 1.37 meters to millimeters. Explain how you got your answer. • 1.37 meters = 1370 millimeters • Convert 2.6 m to centimeters. Explain how you got your answer. • 2.6 m = 260 centimeters • Convert 12.08 millimeters to meters. • 12.08 mm = 0.01208 meters Concept Development – Problem 3 A cat weighs 4.5 kilograms. Convert its weight to grams. A dog weighs 6700 grams. Convert its weight to kilograms. • Work with a partner to find both the cat’s weight in grams and the dog’s weight in kilograms. Explain your reasoning with an equation using an exponent for each problem. • 4.5 kg x 10? = ______ g • 6700 g ÷ 10? = ______ kg • What is the conversion factor for both problems? • Now convert 2.75 kg to g and 6007 g to kg. • 2.75 kg x 10? = ______ g • 6007 g ÷ 10? = ______ kg • • What is the conversion factor for both problems? Let’s relate our meter to millimeter measurements to our kilogram to gram conversions. Concept Development – Problem 4 • The baker uses 0.6 liter of vegetable oil to make brownies. How many millimeters of vegetable oil did he use. • 0.6 l x 10³ = 600 ml • He is asked to make 100 batches for a customer. How many liters of oil will he need? • 0.6 l x 10² = 60 l • After gym class, Mei Ling drank 764 milliliters of water. How many liters of water did she drink? • 764 ml ÷ 10³ = 0.764 l • What do you notice with measurement conversions thus far? Place Values of Metric Prefixes dm dg dL cm cg cL Thousandth m g L Hundredth Tenth dkm dkg dkL One hm hg hL Ten Hundred Thousand km kg kL mm mg mL Concept Development – Problem 4 • Convert 1,045 ml to liters. • 1,045 ml ÷ 10³ = 1.045 l • Convert 0.008 liters to milliliters. • 0.008 l x 10³ = 8 ml