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# 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?

### 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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