Fraction to Hexadecimal Fraction

Example Conversion

Convert the decimal fraction 0.289 to a hexadecimal fraction.

Multiply by 16: 0.289 * 16 = 4.624 the integer part is 4, remainder: 4.624 - 4 = 0.624
Multiply the remainder by 16: 0.624 * 16 = 9.984 the integer part is 9, remainder: 9.984 - 9 = 0.984
Multiply the new remainder by 16: 0.984 * 16 = 15.744 the integer part is 15 ('F' in hex), remainder: 15.744 - 15 = 0.744
Multiply the new remainder by 16: 0.744 * 16 = 11.904 the integer part is 11 ('B' in hex), remainder: 11.904 - 11 = 0.904
Multiply the new remainder by 16: 0.904 * 16 = 14.464 the integer part is 14 ('E' in hexadecimal), and the remainder is 14.464. - 14 = 0.464
Multiply the new remainder by 16: 0.464 * 16 = 7.424 the integer part is 7, remainder: 7.424 - 7 = 0.424
The process can continue, but let's stop here.  
Reading the integers in order: 0.49FBE7 

The decimal 0.289 is approximately 0.49FBE7 in a hex fraction.

Convert the hexadecimal fraction 0.3A to a proper fraction with a numerator and denominator in hexadecimal.

In hexadecimal, 3 represents 3 in decimal, and A represents 10 in decimal.
Convert to decimal fraction:
0.3A16 = 3 * 16 -1 + 10 * 16 -2 = 3/16 +10/256 = 48/256 + 10/256 = 58/256
Simplify the decimal fraction:
58/256 = 29/128
Representation in hexadecimal:
decimal 29 = hex 1D
decimal 128 = hex 80 
29/128 10  = 1D/80 16

This conversion shows that 0.3A in hexadecimal is equivalent to 1D/80 in hexadecimal fraction notation.

Decimal System - Base-10

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