00:01
So this problem is asking us to represent 1 over 7 and 4 over 27 as infinite repeating decimals.
00:15
And in order to do that, we're simply just going to do some long division.
00:22
It will be a little tedious for some of them, but this is probably the most surefire way to do it.
00:34
So having this set up, i took the liberty of putting a bunch of zeros after this decimal point, just to make it easier later on.
00:44
So if we just do long division like we normally would, we'd know that 7 doesn't go into 1, but it goes into 10.
00:55
So that's a 1 there.
00:58
We'd end up with a 3, and 7 doesn't go into 3, so we have to carry down a 0.
01:04
7 goes into 304 times and then we carry down the 0 again because 7 doesn't go into 2 7 goes into 20 twice 14 carry down the 0 because it doesn't go into 6 7 goes into 68 times 56 gives us with 4 7 doesn't go into 4 carry down another 0 7 goes into 40 5 times it gives us 5, and i'll just erase a little bit up here just so we can save some room.
02:13
So we'd end up with 40 minus 35, and that gives us a 5, carry down a 0.
02:20
7 goes into 50, 7 times.
02:25
9.
02:28
And if you notice, we started off with a 1, and now we have a 1 again...