Concepts

In a multi-digit number, the number to the left is ten times the value of the number directly to the right. Multiplying and dividing by powers of ten shifts numbers into different place values. Multiplying increases the number’s value while dividing decreases the number’s value.

Rules

When multiplying by powers of ten, move the decimal place value to the right for every zero in the power of ten. When dividing by a power of ten, move the decimal place value to the left for every zero in the power of ten

Example

Complete the multiplication pattern.

Solution

15 × 1 = 15 × 1. Since 15 is multiplied by one, its place value remains the same.

15
15 × 1 = 15 × 1 = 15

15 × 10 = 15 × 10. Since 15 is multiplied by one ten, it increases in place value by one place to the right of the decimal point.

$(15.\stackrel{\curvearrowright }{0})$
15 × 100 = 15 × 10 = 150

15 × 100 = 15 × 10 × 10. Since 15 is multiplied by two tens, it increases in place value by two places to the right of the decimal point.

$(15.\stackrel{\curvearrowright }{0}\stackrel{\curvearrowright }{0})$
15 × 100 = 15 × 10 × 10 = 1,500

15 × 1,000 = 15 × 10 × 10 × 10. Since 15 is multiplied by three tens, it increases in place value by three places to the right of the decimal point.

$(15.\stackrel{\curvearrowright }{0}\stackrel{\curvearrowright }{0}\stackrel{\curvearrowright }{0})$
15 × 1,000 = 15 × 10 × 10 × 10 = 15,000

Prerequisite Skills

None