For denominators 2, 4, 8, 16, 32, 64 and 128,
depending on the closest match, as in these examples:

0.476823 61/128
0.513072 33/64
0.158690 5/32
0.689468 11/16
0.877029 7/8
0.746163 3/4
0.501050 1/2

Insert Name Define
input Refers to: 0.476823
bse Refers to: =2^(ROW(INDEX(A:A,1):INDEX(A:A,8))-1)
mult Refers to: =ROUND(input*bse1,0)/bse1
err Refers to: =ABS(input-mult)
merr Refers to: =MIN(err)

Paste this array formula into a cell next to input:
=INDEX(mult,MATCH(merr,err,0))
and Format Cells Fraction Up to 3 digits