# Simple math: how to extract the fractional portion from a decimal

Mathematically how do I get the cents from a dollar value (ex: $21.99$)?

As a programmer, I would simply convert to a string and grab everything after the decimal... but I would think this would be doable with pure math, or maybe I have too much faith in the black magic

EDITED

I wasn't clear.
Is it possible with pure math (no computer API.. just old school paper and pencil) to find the fractional part of any given decimal with any given precision?
Is there a formula?

Given xx.yyyy is there a formula that would return yy?

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See the floor or ceil functions and subtract the appropriate one. –  Raymond Manzoni Apr 1 '13 at 15:26
@RaymondManzoni I'm looking for the "math". I can get around an API –  kevcoder Apr 1 '13 at 15:44
Now, if you're just interested in dollar values, and you avoid fractions of a cent, then this is less complicated, but still not reachable through basic arithmetic only. Note that $\$21.99$is simply an alternative notation for the dollar amount $$21+\frac{99}{100}.$$ Multiplication by$100$yields the integer$2199,$whose remainder when divided by$100$is$99$, which upon multiplication by$.01$yields the fractional part. In general, given a dollar amount$d$with no fractions of a cent, $$.01*\text{mod}(100*d,100)$$ will be your fractional part, where$\text{mod}(m,n)$represents the remainder when a positive integer$m$is divided by a positive integer$n$. - thanks for the detailed explanation – kevcoder Apr 1 '13 at 18:02 add comment Look at the number Mod 1. When you look at a number Mod n, you just divide by n, and look at the remainder. So here you divide by 1, and the remainder is just the fractional part. - add comment The best way to do this depends on the language. For something C- or Java-based, I'd do:  decPart = x - (int)x;  Basically, this finds the difference between the integer part and the original number. - add comment You just subtract the integer part, getting$0.99$. If you intend to ask how to do it with some specified set of functions, you posting doesn't make that clear. For example, one could multiply it by$100$(so that$21.83$becomes$2183$), then find the remainder on division by$100$(so that$2183$becomes$83$), then divide by$100$(so that$83$becomes$0.83$). Or, if what you have is the floor function, you could find$x-\lfloor x\rfloor\$, for example: $$21.83-\lfloor21.83\rfloor = 0.83.$$