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Multiply Greater Number by Powers of 10

Sep 20, 2022
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Key Concepts

  • Use pattern and mental math to multiply a whole number by a power of 10

Multiply greater number by powers of 10 

A power of 10 is any of the integer powers of the number ten; in other words, ten multiplied by itself a certain number of times.  

The first few non-negative powers of ten are: 1, 10, 100, 1,000, 10,000, 100,000, 1,000,000,  

10,000,000. 

Below image express expanded form and exponents of 10. 

 expanded form and exponents of 10. 

Below image indicates the power of 10. 

parallel
 the power of 10. 
 the power of 10. 
 the power of 10. 

For example: 

The place value chart shows relationship for the number 4. 

For example: 

Use pattern and mental math to multiply a whole number by a power of 10 

Example 1: 

Power of 10 using place value relationship: 

Find 26 x 10, 000 by using place value relationships. 

parallel

Solution: 

Multiply 26 by 1; 10; 100 and 10, 000; 

26 x 1 = 26 ones = 26 

26 x 10 = 26 tens = 260 

26 x 100 = 26 hundreds = 2,600 

26 x 1,000 = 26 thousands=26, 000 

26 x 10, 000 = 26 ten thousand =260,000 

Pattern 

Pattern 

Power of 10 using exponents 

Power of 10 using exponents 

Exponent: 

An exponent tells how many times a number is multiplied  
by itself. 

10×10×10×10×10×10×10×10×10  

1,000,000,000  

Find 26 x 10, 000 by using exponents. 

Solution: 

Multiply 26 by 1; 10; 100 and 10, 000; 

26 x 1 = 26 x 100 =26 

26 x 10 = 26 x 10 1 = 260 

26 x 100 = 26 x 102 = 2,600 

26 x 1,000 = 26 x 103=26, 000 

26 x 10, 000 = 26 x 104 = 260,000

exponents

Example 2: 

Power of 10 using place value relationship: 

Find 67 x 10, 000 by using place value relationships. 

Solution: 

Multiply 67 by 1; 10; 100 and 10, 000; 

67 x 1 = 67 ones =67 

67 x 10 = 67 tens = 670 

67 x 100 = 67 hundreds = 6,700 

67 x 1,000 = 67 thousands=67, 000 

67 x 10, 000 = 67 ten thousand =670,000 

Pattern 

product ends

Power of 10 using exponents. 

Find 67 x 10, 000 by using exponents. 

Solution: 

Multiply 67 by 1; 10; 100 and 10, 000; 

67 x 1 = 67 x 100 = 67 

67 x 10 = 67 x 10 1 = 670 

67 x 100 = 67 x 102 = 6,700 

67 x 1,000 = 67 x 103 = 67, 000 

67 x 10, 000 = 67 x 104 = 670,000 

exponents
Solution:

Example 3: 

Find 8 x 1,000 using exponent form. 

Example 3: 

Exercise

  • Find each product.
  1. 34 × 1
  2. 34 × 10
  3. 34 × 100
  4. 1, 000
  • Find the value of the following exponents.
  1. 42 × 1
  2. 42 × 101
  3. 42 × 102
  4. 42 × 103
  • Use reasoning to fill in the missing numbers.
  • 245 × 104= ____________.
  • 16 × ________ = 16,000.
  • Explain how to find the product of 80 × 104.
  • Find the product of 60 × 10,000.
  • How many zeros will there be in the product of 17 × 1, 000?
  • Rewrite the following numbers using powers of ten.

For example, 800 = 8 × 102

  1. 9,000
  2. 70,000
  3. 8,000,000
  • If a Robert house manufactures 100 T-Shirts in a day. How many shirts were manufactures in the month of November?
  • Match the powers of 10.
Match the powers of 10.
  • If a Kara runs 10 miles in a day. How many miles Kara runs in 60 days?
  • How many zeros will there be in the product of 19 x 10, 000?

Concept Map

Concept Map

What have we learned

  • Understand Multiply greater number by powers of 10.
  • Understand how to use pattern and mental math to multiply a whole number by a power of 10.
  • Understand how to multiply Power of 10 using place value relationship.
  • Understand exponent.
  • Understand how to multiply Power of 10 using exponents.

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