Place Value
Exponents & Powers of 10
Multiplication Patterns
Critical Thinking
Vocabulary
100

What is the value of the digit 7 in the number 47,382?

  1. 7
  2. 700
  3. 70,000
  4. 7,000

D. 7,000

100

What is the value of 10^3?

  1. 1,000
  2. 100
  3. 10,000
  4. 10


A. 1,000

100

What is the result of 6 × 10^3?

  1. 60
  2. 6,000
  3. 600
  4. 60,000

B. 6,000

100
What happens the place values as they move on the place value chart? 

As we move to the left on the place value chart, the value increases by 10 times; however, as we move to the right on the place value chart the value decreases by 1/10.

100

This is a way to write whole numbers by finding the sum of each digits value. 

expanded form 

200

300 is 1/10 the value of ______________.

3,000

200

What does the exponent in 10^6 tell you?

  1. How many zeros are in the product
  2. How many times to multiply 10 by itself
  3. The number of tens in the number
  4. The number of hundreds in the number

Both A (How many zeros are in the product) & B (How many times to multiply 10 by itself.)

200

What is the product of 12 × 10^2

1,200

200

 In the number 6,420, how does the value of the 4 compare to the value of the 2? Explain

  1. The 4 is 10 times greater than the 2
  2. The 4 is 10 times less than the 2
  3. The 4 and 2 have the same value
  4. The 2 is 100 times greater than the 4

A. The 4 is 10 times greater than the 2

The 4 is in the hundreds place and the 2 is in the tens place. We know that as we move left on the place value chart each place gets 10 times greater. Since the hundreds place is the next left place after the tens it is 10 times greater. 

200

This is a way to represent how many times a base is multiplied. 

exponent 

300

Write the number 6,305 in expanded form.

6,000 + 300 + 5 

(6 x 1,000) + (3 x 100) + ( 5 x 1) 

300

Write 100,000 as a power of 10. (exponential form) 

10^5

300

Solve: 

(7 x 3) x 10 ^ 5 = ? 

2,100,000

300

How does multiplying a number by 10^3 change its value?

Multiplying a number by 10^3 increases its value by 1,000 times, or moves the digits three places to the left.

300
This is a group of three digits within a whole number, typically separated by a comma.

period

400

If you move the digit 5 in 5,000 one place to the right, what is its new value?

  1. 500
  2. 50,000
  3. 5
  4. 5,000

A. 500

400

Write  10^2 in standard form, word form, and expanded form. 

100

ten squared 

10 x 10 


400

Solve:

(5 x 2) x 10 ^ 3 

10,000

400
What can be true for a product of any factor times 1,000? 

The product will always contain three zeros because we are increasing its value by 1,000 times. 

400

Understanding that each digit in a whole number has a specific value based on its location.

Place Value 

500
one million, four hundred eight thousand, six hundred twelve. 


Write this whole number in standard and expanded form. Which digit is located in the ten thousands place and what is its value? 

1,408,612

1,000,000 + 400,000 + 8,000 + 600 + 10 + 2

(1 x 1,000,000) + (4 x 100,000) + (8 x 1,000) + (6 x 100) + (1 x 10) + ( 2 x 1) 


The digit in the ten thousands place is 0 and its value is also 0 since the digits 0 represent a value of nothing.

500

 Which of the following is equal to 1,000,000?

  1. 10^5
  2. 10^7
  3. 10^6
  4. 10^4

C. 10^6

500
What is missing from the equation? 


( ____ x 3) x 10 ^__ = 2,400

( 8 x 3) x 10 ^2 = 2,400

500

Would (5 x 3) x 10^2 and (5 x 6) x 10^2 have products with the same amount of zeros? Explain 

No, even though they are both being multiplied by 100 or 10^2 the base facts are different. 5 x 3= 15 and 5 x 6 =30. The product 30 adds another zero so (5 x 3) x 10^2 = 1,500 and (5 x 6) x 10^2 = 3,000. 

500

This is composed of a base and exponent. Another way to represent repeated multiplication. 

Power

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