Long Division: Repeated Decimals

Lesson Plan - Get It!

Audio:

When you think about it, forever is a very long time. But don't think too hard—it could take forever!

Take a look at how a division problem can represent....forever.

Set up a long division problem: 0.1 divided by 0.3.

• What do you do first?

To make dividing easier, shift the decimal in the divisor to the right until it’s a whole number. Here, you only need to move it one place.

Remember, if you shift the decimal in the divisor, you have to do the same for the dividend. So, move the decimal one place to the right for 0.1 as well.

Now, divide as you normally would.

• How many times can 3 go into 1?

It can't, so you must add a zero to make it 10.

• How many times can 3 fit into 10?

That's right! 3 times, because 3 x 3 is 9.

Place a 3 on top and write 9 underneath to subtract.

You know that 10 - 9 equals 1. Because 3 cannot fit into 1, you must bring down another zero.

• Do you see a pattern?

Once again, 3 fits into 10 three times, giving you another 3 up top.

• What do you notice about the problem?

Yes! This pattern repeats. You’ll continue with 10 - 9 = 1 again and again, leading to 3 after 3 after 3 in the answer.

This means the answer is 0.33333 repeating.

• How do you write the answer?

When a quotient has a repeating decimal, use a line over the repeating digit.

Try another one: 0.555 divided by 0.27.

As before, make the divisor a whole number by moving the decimal two places to the right, and do the same to the dividend.

Now divide as usual.

• How many times can 27 go into 55?

Think of 27 as close to 25 and 55 as close to 50. Start with 27 x 2 and see how that fits.

27 x 2 is 54, so that is as close as possible. Place the 2 up top and 54 below to subtract.

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