# What are the numbers before and after the decimal point referred to in mathematics?

Sorry for asking such a basic question - but is there an actual term for the numbers that appear before and after the decimal point? Example:

25.18

I know the 1 is in the tenths position, the 8 is in the hundredths position. are there singular terms which apply to all of the numbers that appear both before and after the decimal point?

I'm building a billing system, storing dollars and cents as integers (in separate columns), but for other currencies "dollars" and "cents" are not the correct terms = ). Thanks!

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The part after the decimal is sometimes called the Mantissa. There are also articles on the Fractional Part and Integer Part on Wolfram which might be helpful. –  yunone Sep 13 '11 at 0:37
The part before the decimal is sometimes called the Characteristic. –  user02138 Sep 13 '11 at 0:39
Thanks for the help! –  Calvin Froedge Sep 13 '11 at 1:04
I have to say $n$ and $\varepsilon$. –  Raphael Jan 20 '12 at 18:57
BTW, the most common reason people used to learn these terms is that they were using tables of logarithms. –  Ben Crowell Feb 9 '12 at 3:09

There are two terminologies that I'm familiar with. Sometimes, the part to the right of the decimal (cents) is called the mantissa, and the part to the left (dollars, in your metaphor), is called the characteristic.

But I also like the generic terms integer-part and fractional-part. It's what I and those with whom I do research call them (who uses the work mantissa routinely? not me, but perhaps someone). Yes, I know the fractional part doesn't actually have to be a fraction, but that's just something I toss into my big bag of math vagaries.

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Thanks, dude! Appreciate the help. –  Calvin Froedge Sep 13 '11 at 1:05
For what it's worth, in the context of floating-point computer arithmetic, "mantissa" is standard terminology for the "234" part of exponential notations such as "$1.234\times 10^{56}$". –  Henning Makholm Sep 13 '11 at 1:22
The integer and fractional parts of -2.3 are -3 and .7, respectively, despite what some calculators say. What are the characteristic and mantissa of -2.3, I wonder. –  Gerry Myerson Sep 13 '11 at 1:41
@Gerry: Oh, good point. I hadn't thought of that. I do number theory - we don't believe in negative numbers ;p –  mixedmath Sep 13 '11 at 1:42
According to MathWorld, the mantissa of a real number is $x - \lfloor x\rfloor$, so the mantissa of -2.3 is 0.7. On the other hand, MathWorld disagrees with @Gerry (and according to the linked article itself, with probably most mathematicians) in defining the "fractional part" of negative numbers to be $x - \lceil x\rceil$, which would give the fractional part of -2.3 to be -0.3. I assume this convention is due to some implementation convenience for Mathematica. –  Willie Wong Sep 13 '11 at 1:54

Since the term "Mantissa" can refer to the "Fractional part" of the number for logs, and it can also refer to the "Integer part" and "Fractional part" of the number (combined, without the "Exponent part") for numbers in scientific notation and floating point... it is an ambiguous term and should be avoided.

"Significand" is also not appropriate since it also refers to the "Integer part" and "Fractional part" of the number (combined, without the "Exponent part"), for numbers in scientific notation and floating point.

I prefer to use the terms "Integer digits" and "Fractional digits" (or "Integer part" and "Fractional part").

As far as the method to capture the "Integer digits" and "Fractional digits" for a negative number. Given a negative number like n = -2.3:

(Perhaps this is not important to you because your numbers (data) may all be positive numbers).

Method 1:
While it may be correct from a purely technical or academic standpoint to split this up as:
"Integer digits" = (-)3
"Fractional digits" = (+).7

It may not make sense for you depending on how you will use it.

If you will be treating these parts of the number, also as numbers (rather than "Strings"), and you will at some time combine these two number parts back into the original number, this method has the advantage that you can simply add the two parts of the number together to get the original number back: (-)3 + (+).7 = (-)2.3.

Method 2:
You could get the same effect by storing the sign of the number with each part of the number:
"Integer digits" = (-)2 "Fractional digits" = (-).3

This will also allow you to simply add the two parts of the number together to get the original number back: (-)2 + (-).3 = (-)2.3.

But, perhaps your purpose of breaking the number up is to facilitate displaying the number in a particular way. Neither of these methods would be very useful for this purpose, particularly if you were storing the number parts as strings. Storing the number parts using the first method would take some odd Mathematical gymnastics to get a printable version of the number back.

My recommendation is Method 3:
Split the number up like this:

1. Given a number "n" like n = -2.3 or n = 2.3
2. Store the "Sign" of the number:   s = Sgn(n)
Or as boolean:   s = (n >= 0)
3. Remove the "Sign" of the number   n = Abs(n)
4. Save "Integer digits" portion:   i = Fix(n)
5. Save "Decimal digits" portion:   d = n - i
Or as "String":   d = Mid(CStr(n - i), 3)
Or as "Integer":   d = ((n - i) * 10000)
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