00:01
For this problem, we are asked to convert the decimal 15 .7231 to 331 into a rational fraction.
00:09
To begin, we should note that our repeating unit in the decimal is this 231.
00:14
So we can write our decimal as x equals 15 .7 -231 and put our repeating line over top the 231, indicating that's what's getting repeated.
00:25
Now, what we'll want to do first is multiply both sides by some.
00:30
So that we'll get the non -repeating part on one side of the decimal place.
00:36
So, or on the left side is what we'd want.
00:39
So multiplying by 10, we'd get that 10x equals 157 .231 repeating.
00:49
At this point, we can rewrite our 10x additionally as being equal to 157, the integer part, plus 0 .231 repeating infinitely.
01:01
So essentially we have the integer part and we have the repeating tail.
01:05
Now what we can do additionally is we can multiply both sides of the 10x equation.
01:13
Essentially we want to multiply such that we can get one full repetition of 157231 as an integer...