Multiply and divide decimals by 10, 100, and 1000

The rule or shortcut for multiplying and dividing decimals by 10, 100, and 1000 is really easy: you just move the decimal point as many steps as you have zeros in the power of ten. But do you know what this rule is based on? We look at that concept using PLACE VALUE CHARTS.

The rule says that if you're multiplying, you move the decimal point to the right (so as to make the number bigger), and vice versa for division. But in reality, it's not the POINT that is moving, but the NUMBER itself is moving within the different places. We can see this clearly by placing the number in a place value chart or table and considering what happens in the multiplication or division, place by place.

This lesson is meant for 5th grade and onwards.

In the second part of the lesson, we continue practicing multiplying and dividing decimals by powers of ten. This time, the practice problems use an exponent, such as 0.245 × 10⁵. We also look briefly at whole-number divisions where the divisor is a power of ten.

See also

Multiply & divide decimals by powers of ten — online practice

Divide decimals with mental math: sharing divisions — video lesson

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