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 ÷ 1000 = 0.837 Now show 0.418 x 1000. 0.418 x 1000 = 418

Write the Unit as a Decimal 9 tenths = _____ 57 hundredths = ____ 10 tenths = ____ 42 hundredths = ____ 20 tenths = ____ 9 thousandths = ____ 30 tenths = ____ 10 thousandths = ____ 70 tenths = ____ 20 thousandths = ____ 9 hundredths = ____ 60 thousandths = ____ 10 hundredths = ____ 64 thousandths = ____ 11 hundredths = ____ 83 thousandths = ____ 17 hundredths = ____

Write in Exponential Form 100 = 10? Write 100 in exponential form. 100 = 10² 1,000 = 10? Write 1,000 in exponential form. 1,000 = 10³ 10,000 = 10? Write 10,000 in exponential form. 10,000 = 10⁴ 1,000,000 = 10? Write 1,000,000 in exponential form. 1,000,000 = 10⁶

Converting Units 1 km = _____ m 1 kg = _____ g 1 liter = ____ ml Fill in the missing number. 1000 m 1 kg = _____ g 1000 g 1 liter = ____ ml 1000 ml 1 m = _____ cm 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. 0 m 2 m 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. 0 m 2 m 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. 0 m 0.5 m 1 m 1 m 37 cm 1.5 m 2 m 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 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 Thousand Hundred Ten One Tenth Hundredth Thousandth km kg kL hm hg hL dkm dkg dkL m g L dm dg dL cm cg cL 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