## 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 10^{0} =26

26 x 10 = 26 x 10 ^{1} = 260

26 x 100 = 26 x 10^{2} = 2,600

26 x 1,000 = 26 x 10^{3}=26, 000

26 x 10, 000 = 26 x 10^{4} = 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 10^{0} = 67

67 x 10 = 67 x 10 ^{1} = 670

67 x 100 = 67 x 10^{2} = 6,700

67 x 1,000 = 67 x 10^{3} = 67, 000

67 x 10, 000 = 67 x 10^{4} = 670,000

**Example 3:**

Find 8 x 1,000 using exponent form.

## Exercise

- Find each product.

- 34 × 1
- 34 × 10
- 34 × 100
- 1, 000

- Find the value of the following exponents.

- 42 × 1
- 42 × 10
^{1} - 42 × 10
^{2} - 42 × 10
^{3}

- Use reasoning to fill in the missing numbers.
- 245 × 10
^{4}= ____________. - 16 × ________ = 16,000.
- Explain how to find the product of 80 × 10
^{4}. - 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 × 10^{2}

- 9,000
- 70,000
- 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.