How to Multiply Decimals

Multiplying decimals isn’t much different from multiplying multiple digit whole numbers, but there are a few extra steps to keep in mind. The basic steps look like this…

1. Multiply just like you would a multiple digit problem, ignoring decimals for now.
2. Count the number of decimal places in each number of the problem.
3. Put the decimal in the product that number of place values to left of the first digit.

These steps might seem a little vague at first so lets break them down.

Multiply the Numbers and Ignore the Decimals

When we ignore the decimal places (for now), the problem starts to look a lot like multiple digit multiplication, and this step should be pretty familiar to you. If you need help see these other posts on how to multiply multiple digit numbers or given this handy multiplication calculator a try to see details on how to do the work.

Count the Decimal Places

Now that you have a product, you need to put the new decimal place in the right place. In the first step of this process, you go back to the numbers in the problem and count how many place values are to the right of each decimal place.

Place the Decimal in the Product

Once you know the number of decimal places from the prior step, you count over that number from the right-most digit in the product and place the decimal place there.

But what if you don’t have enough digits in the product to count over? This can happen if you are multiplying very small decimal amounts (say, “0.0001” or similar numbers with lots of zeroes). In these cases you may get what looks like a small number of digits in the product, but you will have counted far more decimal places.

To resolve this, you can add as many digits to the left of the number to fill in needed place values. In fact, by convention you should add one extra zero if needed to insure you have at least a zero digit in the ones place value so that your answer doesn’t start with a decimal point as it’s first character.

Can’t I Just Multiply Decimals with a Calculator?

Learning how to multiply decimals by hand is an important skill, and you should master it before relying too much on a calculator if for no other reason than you’ll be able to recognize when your calculator is giving you reasonable answers for problems.

It’s very easy to make mistakes when entering decimal numbers on a calculator, especially numbers with lots of repeated zeros. Knowing intuitively what looks like a reasonable answer and a reasonable number of decimal places will save you a lot of trouble, which makes learning this manual multiplication process far more valuable than you might first think.

Wait, Do I Need to Line Up the Decimals?

Sometimes students are confused when multiplying decimal numbers because when you add or subtract decimals, you need to be super careful to line up the decimals and place values. If you don’t do this step in addition and subtraction, you can wind up mixing up different place values (for example, subtracting tenths from hundredths or other mismatches).

Fortunately, when we multiply decimal numbers we don’t need to worry about this. The step where we count the decimal places in the original problem numbers and then move the decimal to its correct position in the product adjusts for everything without needing to line up decimals before hand.

Multiplying Decimals is Easy if You Practice

These steps may seem a lot more complicated than multiplying whole numbers, but with a bit of practice it becomes a lot easier. There are a number of multiplication with decimals worksheets online that can be used to help master this skill, or check out the remaining posts below for more details on specific decimal multiplication strategies!