What is the fractional equivalent of 1.37?

This requires some algebra to perform.
You want to define the repeating decimal that you are calculating as x.
In this case, x = 0.137373737...
Now you multiply that times a power of 10 in order to move the decimal place to the right of the last repeating number in the deicmal.
In this case,
137.37373737... so it would be 1000x since you had to move the decimal 3 places to the right.
now multiply by a power of ten to just before the first digit of the repeating part of the decimal.
1.3737 This would be 10 since 0.137373... * 10 = 1.373737... so 10x
Now you use algebra and get
1000x - 10x = 137.3737... - 1.3737...
The effect is to remove the repeating part from the equation to yield:
990x = 137 - 1 = 136
The fraction is then x = 136/990
this factors down to 68/495
now remember that you have to add one times the denominator (495) to the numerator and you end up with:
563/495