Lesson 1: Multiply Greater Numbers by Powers of 10

Property

Multiplying a whole number by a power of 10 ($10, 100, 1000, \dots$) involves annexing (adding) zeros to the end of the number. The number of zeros added is equal to the number of zeros in the power of 10.

• $n \times 10 = n0$
• $n \times 100 = n00$
• $n \times 1000 = n000$

Examples

• $5 \times 10 = 50$
• $82 \times 100 = 8200$
• $45 \times 1000 = 45000$

Explanation

When you multiply a whole number by 10, 100, or 1000, you are making the number that many times larger. This has the effect of shifting each digit to a larger place value. A simple way to find the product is to count the number of zeros in the power of 10 and add that many zeros to the end of the original number.

Property

To multiply a whole number by a power of 10 written with an exponent, $10^n$, annex $n$ zeros to the end of the whole number.

Examples