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