Example conversion:
22.657 decimal feet
With the whole feet amount of 22, you don't have to do anything. Remove the 22 from this amount
22.657 - 22 = 0.657
That leaves 0.657 decimal feet
Remove the whole inches from this amount by multiplying 0.657 by 12 (there are 12 inches in one foot)
0.657 * 12 = 7.884
The 7 is the whole inch amount.
Subtract the 7 inches from 7.884
7.884 - 7 = 0.884
0.884 is a fraction of an inch in decimal format, and you can write it as 884/1000.
Why is the denominator 1000. The decimal digits have a place value based on their location, and the place value of the last digit in the decimal number determines the denominator of the fraction.
0.884 = the first 8 has a place value of 10, the second 8 has a place value of 100, and the 4 has a place value of 1000. The denominator for this fraction is 1000, and the decimal number is the numerator.
Decimal 0.884 as a fraction is written as 884/1000 simplified to 221/250
This fraction amount of 221/250 of an inch is not very useful for most people. To make it more usable, you have to pick the denominator that works for you. And the higher the denominator, the more accurate the fraction will be.
Conversion to a usable fraction;
0.884 decimal inches
8 = the denominator.
Multiply the decimal 0.884 by 8, and round the result to the nearest whole number to get the numerator of this fraction;
0.884 * 8 = 7.072 rounded to 7
7 is the numerator
0.884 inches with an 8 as the denominator is written as 7/8
Decimal 0.884 inches
16 as the denominator.
Multiply the decimal 0.884 by 16
0.884 * 16 = 14.144 rounded to nearest whole number = 14
0.884 decimal inches with 16 as the denominator is written as 14/16, simplified to 7/8
Adding the results together;
The decimal feet amount of 22.657 = 22' - 7 -7/8"