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# Multiplying by Powers of 10

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In this section, we continue to expand our knowledge of multiplication with whole numbers. We will focus on multiplying by powers of 10. Specifically, we can use this technique as a shortcut for multiplying large multi-digit whole numbers with 1 or many trailing zeros. This technique greatly reduces the amount of time it takes to multiply when these scenarios occur. A trailing zero or trailing zeros are zeros that occur at the end of the number and are not interrupted by a non-zero digit.

For example, the number 23,000 has 3 trailing zeros or 3 zeros at the end of the number. Notice how these zeros are not interrupted by a non-zero digit.

As another example, the number 23,030 has only 1 trailing zero. The 3 in the tens' place is a non-zero digit and thus interrupts the pattern of zeros.

When we multiply two or more numbers with trailing zeros, we chop off the trailing zeros and multiply the resulting numbers. Once this is done, we attach the total number of trailing zeros between all factors to the end of the product.

For example, the number 23,000 has 3 trailing zeros or 3 zeros at the end of the number. Notice how these zeros are not interrupted by a non-zero digit.

As another example, the number 23,030 has only 1 trailing zero. The 3 in the tens' place is a non-zero digit and thus interrupts the pattern of zeros.

When we multiply two or more numbers with trailing zeros, we chop off the trailing zeros and multiply the resulting numbers. Once this is done, we attach the total number of trailing zeros between all factors to the end of the product.

Multiplying by Powers of 10 Resources:

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