Step 1:
The first step to converting 213.77101531413 to a fraction is to re-write 213.77101531413 in the form p/q where p and q are both positive integers. To start with, 213.77101531413 can be written as simply 213.77101531413/1 to technically be written as a fraction.
Step 2:
Next, we will count the number of fractional digits after the decimal point in 213.77101531413, which in this case is 11. For however many digits after the decimal point there are, we will multiply the numerator and denominator of 213.77101531413/1 each by 10 to the power of that many digits. So, in this case, we will multiply the numerator and denominator of 213.77101531413/1 each by 100000000000:
Step 3:
Now the last step is to simplify the fraction (if possible) by finding similar factors and cancelling them out, which leads to the following answer for 213.77101531413 as a fraction:
10261/48 / 1