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A Step-by-Step Guide to Dividing Decimals

dividing decimals: person manually solving an equation

Does the idea of dividing decimals bring on confusion and dread? We get it, decimal subtraction and addition is easy enough. But when long division is added to the equation, things suddenly get more complicated.

We're here to tell you that dividing decimals is a lengthy but totally manageable process, and with this guide, you'll be able to divide decimals with ease. Let's get started!

Dividing With Decimals: Where to Start

The goal of the decimal division process is to find the quotient that results from dividing a decimal dividend by a decimal divisor. Let's explain what these terms mean using the following decimal division problem:

decimal division problem

In this equation, 66.82 is the dividend (the value that's being divided) and 3.1 is the divisor (the value that the dividend is being divided by.) The answer that you'll get when you divide the dividend by the divisor is called the quotient.

How to Divide Decimals by Decimals

Now that we've defined the terms, let's walk through each step of decimal division:

dividing decimals: decimal division problem

Step 1: Make a general estimate of what you think the quotient will be. This can be done by rounding both the dividend and divisor to the closest whole number:

rounding off dividend and divisor

Now that these values have been rounded, you can use mental math or a calculator to divide them:

dividing decimals: dividing whole numbers

We've now determined an approximate value of what the quotient should be. This will come in handy later.

Step 2: Move the decimal place of the divisor to the right until it's a whole number. The decimal of the dividend has to move the same number of decimal places. (In this case, that's one digit to the right.)

move the decimal place

As you can see, we’ve moved the decimal one place to the right for both values.

Step 3: Now we can start the division process:

dividing decimals: move the decimal place

Since 31 cannot fit into the value of 6, we need to determine what value we can multiply 31 by to get to close to 65. Multiplying 31 by 2 equals 62, so let's put a 2 above the 65 and subtract the difference:

subract the difference

That gives us 3. Now let's bring the 8 down.

dividing decimals: bring down

Multiply 31 by 1 and subtract this value from 38.

multiply then subtract

Now let's bring down the 2. Multiply 31 by 2 and subtract this value from 72.

dividing decimals: bring down, mutiply and subtract

Let's bring down a zero and multiple 31 by 3. Then, subtract this value from 100.

bring down then multiply then subtract

Bring down another 0. Then subtract 31 multiplied by 2 from 70.

dividing decimals: bring down, multiply, subtract

The remaining amount should be 8. Since we are going to round to the second decimal, we can stop here. We’ll explain this in the next step.

Step 4: The decimal point in the quotient needs to be at the same place as the dividend.

decimal point in the quotient

Though the quotient has three decimal numbers, let's round to the second place value:

dividing decimals: round to the second place

Step 5: Let's compare our quotient to the original estimate in step one to determine if this is a reasonable answer:

compare the quotient vs. the original

Since the difference between 22 and 21.23 is less than one, our answer is indeed reasonable.

Mastering Decimal Division

Once you learn our five-step long division process, you can become the master of decimal division. Mastering this will help you with many other decimal related problems like adding, subtracting, and multiplying decimals.

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