To convert a number in decimal feet format to foot inch and fraction first, remove the foot value. That is the amount in front of the dot. To get the number of inches, multiply the remaining decimal amount by 12. This time the amount before the dot becomes the inch value. The decimal amount that is left is a fraction value of one inch.
If you convert this to a fraction, you can end up with something that isn't very useful, like 2364/3365. The denominator of 3365 has to change to a usable one that you can easily find on your tape measure. 16, 8, 4 2 make good denominators, and if need be more precise, 64 can be the denominator.
To be usable, 16 is a good choice for a denominator and still maintains an acceptable level of accuracy.
Multiply the leftover decimal by 16 and round this number to the nearest whole number. This amount is the numerator of your fraction.
Example:
18.649 decimal feet
The 18 is the foot value, and subtract this from the decimal amount
18.649 - 18 = 0.649
0.649 is the inch value
extract the whole inches of 0.649 by multiplying by 12;
0.649 * 12 = 7.788
The seven before the dot is the full inch value.
Remove this amount from the decimal, 7.788;
7.788 - 7 = 0.788
The remaining decimal 0.788 is a fraction of an inch.
As a fraction, you write it as 788/1000 simplified to 197/250
Not much use, and hard to find a fraction with a denominator of 250 on your tape measure.
You have to pick a denominator that you can use, and in most cases, 16 as the denominator for the fraction is a good choice.
Take a step back to the remaining decimal 0.788. Multiply this amount by 16 and round the result to the nearest whole number to get the numerator of the fraction;
0.788 * 16 = 12.608
In this case, you have to round it upward, and the amount becomes 13.
13 is the numerator value of your fraction.
Collect all the results and place them together;
18.649 in decimal feet becomes 18' 7 13/16"
If you had decided to make the denominator a 2, find the numerator of the fraction by multiplying 0.788 by a 2
0.788 * 2 = 1.576 rounded to the nearest whole number, 2
Now your result would look like 18' 7 2/2" --- 18 feet- 8 inches
Using a smaller denominator here produced a less accurate result.
It is not always the case, but you are often better off using a higher amount for a denominator.
Now let's check this 18' 7 13/16" result for accuracy by converting it to a decimal.
You know that the 18, the foot value, belongs before the dot.
The first part is 18.0000
Take the inch value of 7 and divide this by 12;
7 / 12 = 0.583333333333333 rounded to 0.5833
Add this to the 18.000
18.000 + 0.5833 = 18.5833
One more conversion left;
Take the fraction and divide the numerator by the denominator.
13 / 16 = 0.8125
Because you are converting a fraction of an inch, you have to divide the decimal amount of 0.8125 by 10 (fractions of an inch are in base 10) ;
0.8125 / 10 = 0.08125.
Add this to the previous amount of 18.583
18.5833 + 0.08125 = 18.665 rounded to three digits.
18' 7 13/16" in decimal format is 18.665
Because you are using a usable fraction in the first conversion, there can be a difference in this result;
18.665 - 18.649 = 0.016.
That is a 16/1000 inch difference!
I don"t think you have much to worry about with a difference like that when you are building your home!
Or you let this calculator do it for you!