1. Module 1
Lesson 4
Objective: Use exponents to denote powers of 10 with application to metric conversions.

2. 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

3. 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

4. Multiply and Divide Decimals by 10, 100, and 1000
Using your place value chart, show 837 ÷ 1000.
837 ÷ 1000 = 0.837
Now show x 1000.
0.418 x 1000 = 418

5. 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 = ____

6. 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

7. 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

8. 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.

9. Concept Development – Problem 1
Draw a line 2 meters long.
0 m 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.

10. Concept Development – Problem 1
Draw a line 2 meters long.
0 m 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.

11. 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.

12. Concept Development – Problem 2
Draw a line 1 meter 37 centimeters long.
0 m m m m 37 cm 1.5 m 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

13. 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 millimeters to meters.
12.08 mm = meters

14. 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.

15. 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 = l
What do you notice with measurement conversions thus far?

16. 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

17. Concept Development – Problem 4
Convert 1,045 ml to liters.
1,045 ml ÷ 10³ = l
Convert liters to milliliters.
0.008 l x 10³ = 8 ml