Repeating and Terminating Decimals | Math with Mr. J

In this video, I'm going to cover the difference between repeating decimals and terminating decimals. Now, in simple terms, terminating decimals end. We get to a point where we have a clean-cut zero within our division. Repeating decimals never end. They have a pattern that goes on forever, whether it's one digit that repeats or a group of digits that repeats. Let's jump into our examples and see exactly what a repeating decimal and a terminating decimal look like. And there will be one of each. Now, each example is in fractional form. We are going to divide to get these two decimal forms. So for number 1, we divide 20 by 9. Always do the numerator, the top number, divided by the denominator, the bottom number. So again, 20 divided by 9. So let's set this one up. 20 divided by 9. And we will go through our division process here to see if this is repeating or terminating. 20 divided by 9. How many whole groups of 9 out of 20? Well, 2. 2 times 9 is 18. Subtract. We get 2. Now, we want this in decimal form. So we place our decimal, bring it straight up, and use placeholder zeros to continue our division process. Remember, we're looking for a clean-cut zero here. That will tell us that we have a terminating decimal. A repeating decimal will continue on forever, and you'll see a pattern. So let's see what happens here. 20 divided by 9. Well, that's 2. 2 times 9 is 18. Subtract. We get 2. So we need to continue on. We'll use another zero. Bring that down. So we have 20 divided by 9 again, which is 2. Let me extend this bar here. 2 times 9 is 18. And you'll probably notice a pattern. So 20 minus 18 is 2. We'll use another zero. And this pattern is going to continue on forever. So how many 9s out of 20? 2. 2 times 9. 18. I ran out of room there, but 20 minus 18 is 2. We would bring down another zero. And again, that pattern is going to continue on forever. So this is a repeating decimal. We will have 2s that go on forever. So we can write our answer like this. 2. Decimal. 2. And then put a bar above the decimal portion that repeats. So we have a 2 that repeats. So put the bar above the 2. And that shows that we have a repeating 2. This is called bar notation. So our final answer, 2 and 2 repeating. Let's move on to number 2, where we have 3 eighths, or 3 divided by 8. Let's set this up. So 3 divided by 8. How many whole groups of 8 out of 3? Well we can't do that, so we can put a zero here. We want this in decimal form, so let's place it after the whole number and bring it straight up into our answer. We will use a placeholder zero to continue through our division process. So 30 divided by 8. How many whole groups of 8 out of 30? Well 3. That gets us to 24. 3 times 8, 24, subtract, we get 6. So we did not get a clean cut zero yet, so we need to continue on. So let's put another zero, bring that down. And now we have 60 divided by 8. So how many whole groups of 8 out of 60? Well 7. That gets us to 56. Let me extend here. 7 times 8, 56, subtract, we get 4. So we need to continue on. Zero, bring that down, and we have 40 divided by 8. And this is going to give us our zero. 40 divided by 8 is 5, 5 times 8, 40, 40 minus 40 gives us our clean cut zero. So our final answer is 0.375, 375 thousandths. So that is our final answer, and it is a terminating decimal. We get that clean cut zero. That shows us that we are done, and the decimal has ended. So there you have it. There's the difference between repeating decimals and terminating decimals. And hopefully you saw the difference there as far as, like number 1, we had that pattern that continued on forever and gave us a repeating 2. And then number 2, we got that clean cut zero there at the end finally and gave us a terminating decimal. If you want more examples of repeating decimals, I dropped links down in the description. I hope that helped. Thanks so much for watching. Until next time, peace.