00:01
This problem wants us to write fractions for these repeating decimals.
00:03
So we have 0 .7 repeating.
00:07
Okay, so in order to do this, we can say that our fraction x is equal to 0 .7 repeating.
00:17
Because it's only one digit repeating, i'm going to multiply this by x by 10.
00:23
It's going to give us 7 .7 repeating.
00:27
And then if we subtract x from 10x, we'll have 9x.
00:33
Equals seven and all the point seven repeating will cancel out and so x is just equal to seven -nights so x is seven -ninths that's part a okay part b we have 0 .2 and then the 8 is repeating so in order to cancel this out i'm gonna represent so our x is the 0 .28 repeating so we can write this as 100x equals 28 .8 repeating.
01:20
We're just moving the decimal.
01:23
10x is 2 .8 repeating.
01:28
Kind of following the same algorithm as before.
01:31
We just subtract one from the other trying to eliminate that repeating piece.
01:35
So we're going to have 90x is equal to 26 and therefore x is 26 over 90...