Lesson 4

Objective: Use exponents to denote powers of 10 with application to metric conversions.

MODULE 1

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 = _____• 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.• 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 = _____ mFill in the missing number.

• 1000 m

• 1 kg = _____ gFill in the missing number.

• 1000 g

• 1 liter = ____ mlFill in the missing number.

• 1000 ml

• 1 m = _____ cmFill 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.

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

• 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

Thousand

Hundred Ten One Tenth

Hundredth

Thousandth

kmkgkL

hmhghL

dkmdkgdkL

mgL

dmdgdL

cmcgcL

mmmgmL

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