How to convert floats to human-readable fractions?

Question

Let's say we have 0.33, we need to output "1/3". If we have "0.4", we need to output "2/5".The idea is to make it human-readable to make the user understand "x parts out of y" as a better way of understanding data. I was wondering if there was a simple way to do this?

Answer 1

YES!

consider the following table, which you may have to repair when Wyzant

ruins the formatting. THe labels of the columns represent whether the decimal

stops or repeats. The rows are labeled by # of digits

DECIMAL STOPS | DECIMAL REPEATS

1 digit / 10 | / 9

2 digit / 100 | / 99

3 digit / 1000 | / 999

So in your example, 0.4 is a SINGLE decimal that does not repeat, it stops.

SO you divide that digit by 10.

Then 4/10 = 2/5

FOr x=0.25, it is 2 digit terminating decimal so, per the table, divides by 100.

25/100 is in fact 1/4

Finally, for x=0.125, it is a 3 digit terminating decimal. The table says to divide by 1000.

So 125/1000 reduces to 1/8

Now for the repeating case.

Your examples is x=0.3 = 0.333333....

Note that the digit repeats and does NOT STOP, as you have written

in your example. Since it is a SINGLE repeating digit, the fraction is

3/9 = 1/3, as you stated.

The rule of 9's can be proven algebraically, if you are interested, and

formulas exist for converting such decimals into fractions.

For now, you can get by with just the table.

The only other possibility is the decimal starts out ok,

but then repeats.

For example, 0.83333333 = 0.83

In that case, you must split the decimal into two parts:

0.8 + 0.03

0.8 + (1/10) 0.3 <- multiplies and divides by 10 so that the decimal appears in front of the repeating decimal

0.8 + (1/10)(3/9)

(8/10) + (1/10)(3/9)

(8/10) + (3/90)

(72/90) + (3/90)

75/90

5/6