# 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!

• 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
• 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

## 5 Answers

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 word 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.

• 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
• 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
• @HenningMakholm In computer arithmetic, don't we usually use "Mantissa" for everything except the exponent? This is also what Wikipedia says here: en.wikipedia.org/wiki/Mantissa "The significand of floating-point number or scientific notation". – Jan-Philip Gehrcke Mar 6 '13 at 18:09
• This discussion is not so important to me anyway. But my point was the following: You said "mantissa is standard terminology for the 234 part of exponential notations such as 1.234 × 10e56". According to that wikipedia article, however, the mantissa is the 1.234 part, so including the 1.. That's the difference. – Jan-Philip Gehrcke Mar 7 '13 at 18:48

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)

"scale of a number":

Scale is the number of digits to the right of the decimal point in a number. For example, the number 123.45 has a precision of 5 and a scale of 2.

bc - The arbitrary precision calculator - defines it for us in their documentation. For example, type man bc on your linux terminal

   NUMBERS
The most basic element in bc is the number.  Numbers are arbitrary pre‐
cision numbers.  This precision is both in the  integer  part  and  the
fractional part.  All numbers are represented internally in decimal and
all computation is done in decimal.  (This  version  truncates  results
from divide and multiply operations.)  There are two attributes of num‐
bers, the length and the scale.  The length is the total number of dec‐
imal digits used by bc to represent a number and the scale is the total
number of decimal digits after the decimal point.  For example:
.000001 has a length of 6 and scale of 6.
1935.000 has a length of 7 and a scale of 3.

• Do you have a reference for this terminology? I've never heard it used in this context. – Michael Albanese Jan 26 '16 at 21:09
• I think you should remove your votes to delete this post; I've cited articles that use this term in the computer science field. – activedecay Jan 28 '17 at 3:37

the number before the decimal point is called the whole number while the number after the decimal point is called the part of a whole

...

• See the comments for the correct terms. – Chris Godsil Jun 11 '13 at 0:24

Sometimes, the part to the right of the decimal point is called the mantissa, while the part to the left is called the characteristics.