Multiply Greater Number by Powers of 10

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. 

Below image indicates the power of 10. 

For example: 

The place value chart shows relationship for the number 4. 

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. 

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 

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

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 

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 

Example 3: 

Find 8 x 1,000 using exponent form. 

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.

• 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

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.