Convert one-seventh to a decimal.
So, the way that we’re gonna do this is first by thinking, what does one-seventh mean? Well, one-seventh is the same as one divided by seven. So, we can carry out this calculation to work out what it would be as a decimal. And the method that I’m gonna use to help me do this is short division, also known sometimes as the bus stop method.
So, first of all, I want to see how many sevens go into one. And seven doesn’t go into one, so it’s zero. And we’re gonna have a remainder of one. So, what I do is I carry this across. And as you can see, I’ve also put in decimal points here. And that’s because it’s a decimal, because we’ve looked at the units and now we’re moving on to the tenths. So, now, we go seven into 10. So, that goes one remainder three.
And then, we’re gonna see how many sevens go into 30. And that’s four. And that’s because four sevens are 28. And there’s gonna be a remainder of two. So, then, we’re gonna see how many sevens go into 20, which is two remainder six. And that’s because two sevens are 14 and then add six to get to 20. And then, what we can do is how many sevens go into 60? And that’s eight because eight sevens are 56 and then we’re gonna have a remainder of four.
So, then, it’s sevens into 40. Well, sevens into 40 goes five. And that’s because seven multiplied by five is 35. Then, we’re gonna have remainder five. So, we’re gonna have sevens into 50. Well, this is gonna go seven times because seven sevens are 49. And we got remainder of one. So, we’re gonna have sevens into 10, which is one. And that’s one seven is seven then remainder three because we add three to get to 10. So, then, we’re gonna go sevens into 30, which will be four because seven fours are 28. And that’s remainder two.
And we could see at this point, hold on, we’ve actually started to repeat. And that’s because we’ve got 0.142857 and then we’ve got one, four, and then the next value would be two. And actually, continue the same way because we’ve got the same numbers being carried across. So therefore, this is the something that is known as a recurring decimal.
And a recurring decimal is a decimal that continues the same pattern indefinitely. And a recurring decimal can use a couple of different types of notation. And I’ve shown them here. And they are one with a straight line from the number that is the first number that’s repeated to the last number that’s repeated. And the other is two dots, one above the first and last numbers that are repeated. So therefore, we can say that if we convert one-seventh to a decimal, we get 0.142857 recurring.