The Place-Value Multiplication Trick

A decimal point can make a multiplication look tricky. But watch this... we can move it out of the way without changing the value we are finding. The secret is to keep track of PLACE value.

Think of three point six as thirty-six tenths. The digits are three and six, but their values are three ones and six tenths. So do not report a digit on its own. Ask what PLACE it holds, because that tells you its value. To multiply by a decimal, rename the decimal using place value. Multiply with whole numbers first. Then return the answer to the correct unit. If you renamed the decimal as tenths, your whole-number result counts tenths, not ones. Estimate first. Three point six is close to four. So the exact result should be a little smaller than multiplying by four. The estimate checks the size, while place value fixes the decimal point.

Let's work through an example. Calculate twenty-four multiplied by three point six. First, rename three point six as thirty-six tenths. The decimal point lifts away, but a tenths label stays. Now calculate twenty-four multiplied by thirty-six tenths. Partition thirty-six into thirty and six. Twenty-four multiplied by thirty is seven hundred and twenty. Twenty-four multiplied by six is one hundred and forty-four. The two partial products slide together. Seven hundred and twenty plus one hundred and forty-four equals eight hundred and sixty-four. That eight hundred and sixty-four is a count of tenths. Ten tenths make one whole, so regroup the count in tens. Eight hundred and sixty-four tenths becomes eighty-six point four. The tenths label changes into the decimal answer: eighty-six point four. Check it. Twenty-four multiplied by four is ninety-six. Our answer, eighty-six point four, is smaller. That fits, because three point six is smaller than four. The answer is eighty-six point four.

Rename the decimal by place value, multiply as whole numbers, then restore the unit and estimate to check. You did not guess where the point goes - you PROVED it. Decimal multiplication is under control!