Lesson Objectives

- Demonstrate an understanding of multiplication with multi-digit whole numbers
- Learn how to identify trailing zeros
- Learn how to quickly multiply multi-digit whole numbers by powers of 10

## How to Multiply Multi-Digit Whole Numbers by Powers of 10

When we multiply large multi-digit whole numbers, we will often face numbers with trailing zeros. What is a trailing zero? Trailing zeros are zeros that occur uninterrupted and at the end of the number. Let’s take a look at three different numbers: 5300, 190,000, and 402,000.

5300 - This number has 2 trailing zeros, the 2 zeros occur uninterrupted and at the end of the number.

190,000 - This number has 4 trailing zeros, the 4 zeros occur uninterrupted and at the end of the number.

402,080 - This number has only 1 trailing zero. Although there are 3 total zeros in the number, the first two are not trailing zeros.

When we multiply and there are trailing zeros involved, we can use a shortcut. Let’s take a look at the following scenario:

6 x 10 = 60

13 x 100 = 1300

19 x 1000 = 19,000

3 x 10,000 = 30,000

Each time we multiply here, we can simply exclude the trailing zeros and multiply the remaining numbers. Once this is done, we can attach the total number of trailing zeros to the answer.

What if we asked what is 9 x 100,000?

Cut off the trailing zeros and multiply:

9 x 1 = 9

Then attach 5 trailing zeros to the end:

900,000

9 x 100,000 = 900,000

Example 1: Find the product of 13 x 500

Example 2: Find the product of 2400 x 80,000

5300 - This number has 2 trailing zeros, the 2 zeros occur uninterrupted and at the end of the number.

190,000 - This number has 4 trailing zeros, the 4 zeros occur uninterrupted and at the end of the number.

402,080 - This number has only 1 trailing zero. Although there are 3 total zeros in the number, the first two are not trailing zeros.

When we multiply and there are trailing zeros involved, we can use a shortcut. Let’s take a look at the following scenario:

6 x 10 = 60

13 x 100 = 1300

19 x 1000 = 19,000

3 x 10,000 = 30,000

Each time we multiply here, we can simply exclude the trailing zeros and multiply the remaining numbers. Once this is done, we can attach the total number of trailing zeros to the answer.

What if we asked what is 9 x 100,000?

Cut off the trailing zeros and multiply:

9 x 1 = 9

Then attach 5 trailing zeros to the end:

900,000

9 x 100,000 = 900,000

### Multiplying with Trailing Zeros

- Cut off the trailing zeros from each number and multiply
- Attach the total number of trailing zeros to the end of the answer

Example 1: Find the product of 13 x 500

- Cut off the trailing zeros from each number and multiply
- 13 x 5 = 65
- Attach the total number of trailing zeros to the end of the answer
- 6500

Example 2: Find the product of 2400 x 80,000

- Cut off the trailing zeros from each number and multiply
- 24 x 8 = 192
- Attach the total number of trailing zeros to the end of the answer
- 192,000,000

Ready for more?

Watch the Step by Step Video Lesson Take the Practice Test