Entry Ticket: Multiply and Divide by Powers of 10

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Multiplying by Power of 10

​When you multiply any whole number by a power of 10 (10, 100, 100 or 10¹​, 10² , 10³ ) You add the amount of zeros you see or the amount of zeros that the exponent shows. Also you can place your decimal and move it that many places to the right.​ When you multiply a power of 10 by a decimal you move the decimal to the right depending on the number of zeros you have or by the exponent that is shown.

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Dividing by Powers of 10

When dividing a whole number or a decimal by a power of 10 you add and move your decimal to to the left based on the number of zeros you see or based off the exponent you see.​

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Find 89.5 ÷ 10

• A number divided by 10 is less than the number.

• Moving the decimal point to the left decreases the number's value.

• Place value is based on 10, so dividing by 10 has the same result as moving the decimal point one place to the left.

Notice the patterns in the table.

• 89.5 ÷ 10

• 10 = 10¹

• The exponent tells us to move the decimal point one place.

• Since we are dividing, we move the decimal point one place to the left.

• So, 89.5 ÷ 10 = 8.95

Look for a pattern.

4,600 ÷ 10 = 460

460 ÷ 10 = 46

46 ÷ 10 = 4.6

4.6 ÷ 10 = 0.46

Look for a pattern.

134.4 ÷ 10³ = 0.1344

134.4 ÷ 10² = 1.344

134.4 ÷ 10¹ = 13.44

134.4 ÷ 10⁰ = 134.4

Multiply and Divide by 10, 100, and 1,000

Today we will review what we learned in Lesson 2.

Multiple Choice

7.25 ÷ 10

• 0.725

• 72.5

• 725

Multiplying a decimal by 10 shifts the digits to the left by one space in the place value charts.

Multiple Choice

15.7 ÷ 1,000

• 1.57

• 0.157

• 0.0157

Multiplying a decimal by 100 shifted the digits two spaces to the left on the place value chart.

Multiple Choice

$$10^2$$  

• 100

• 1,000

• 10

• 10,000

Multiple Choice

$$0.004\times1,000=$$

• 0.04

• 0.004

• 4

Multiple Choice

$$10^3$$  

• 10,000

• 100

• 1,000

• 100,000

Multiple Choice

$$1\cdot004\times1,000=$$  

• 104

• 1,004

• 10.04

Multiple Choice

When moving from one place value to the next, by how much do numbers change?

• by 100

• by 1

• by 10

• by 1,000

Answer

Base 10 System

How many fingers do you have?

Why do you think our number system is a base ten system?

Multiple Select

$$1.024\times100=$$  

• 102.4

• 10.24

Exponent:

The little number that tells how many times to multiply the base by itself.

Answer

Multiple Choice

How is 10⁶ written as a product of 10?

• 10 x 10 x 10 x 10

• 60

• 6,000,000

• 10 x 10 x 10 x 10 x 10 x 10

Multiple Choice

$$1.324\times1,000=$$  

• 1,324

• 13.24

• 132.4

Multiple Choice

135 divided by 10

• 13

• 13.1

• 13.5

• 15

Answer

Multiple Choice

5.8 x 100

• 580

• 5.8

• 5,800

• .58

Dividing a decimal by 10 shifts the digits to the right by one place on the place value chart.

Multiple Choice

2.7 x 10

• 270
• 0.27
• 27
• 0.027

Multiple Choice

$$4\cdot1\div10=$$  

• 0.14

• 0.41

• 41

Multiple Choice

7.44 x 1,000

• 7,440

• 744

• 7.44

• 74,400

Dividing a decimal by 10 shifted the digits one space to the right on the place value chart.

Multiple Choice

0.085 x 100

• 0.85

• 8.5

• 85

• 850

Multiple Choice

$$4\cdot1\div100=$$  

• 41

• 4.10

• 0.041

Multiple Choice

17.5 x 1000

• 1.75

• 175

• 17,500

• 0.175

Dividing a decimal by 100 shifted the digits two spaces to the right on the place value chart.

Multiple Choice

7.129 × 100 = 

• 712.9
• 71.29
• 0.7129
• 0.07129

Fill in the Blanks

$41\div1,000=$  

Multiple Choice

Elyse is cutting strips of paper for a scrapbook page. Each strip is 1.5 centimeters wide. How wide will 10 strips of paper be?

• 1.5 centimeters

• 15 centimeters

• 150 centimeters

• 1500 centimeters

Dividing a decimal number by 1,000 shifted the digits three spaces to the right in the place value chart. Dividing by 10, 100, or 1000 caused the numbers to decrease in value.

Multiple Choice

7.129 × 100 = 

• 712.9
• 71.29
• 0.7129
• 0.07129

Multiple Select

$$123\div1,000=$$  

• 123

• 0.123

• 12.3

Multiple Choice

Which power of 10 will make this number sentence true?
0.4 x _____= 4

• 100
• 10
• 1,000
• 0

Multiple Choice

.75 x 10 =

• .75

• 7.5

• 75

• .075

Multiple Choice

When multiplying a decimal by 100, the decimal place moves:

• one place to the right

• two places to the right

• one place to the left

• two places to the left