Fractional Part Function Formula
The formula for the fractional part, denoted as {x} or frac(x), is given by:
{x} = x – ⌊x⌋
In this formula, ⌊x⌋ represents the greatest integer less than or equal to x (the floor function). The fractional part function subtracts the integer part from the original number x, leaving only the decimal part or the fractional component. The result of the fractional part function is always a value between 0 (inclusive) and 1 (exclusive).
Example: Find the Fractional Part Function for x = 4.75
Solution:
Using the fractional part function formula:
{4.75} = 4.75 – ⌊4.75⌋
Now, find the greatest integer less than or equal to 4.75:
⌊4.75⌋ = 4
Substitute this back into the formula:
{4.75} = 4.75 – 4
{4.75} = 0.75
So, the fractional part of 4.75 is 0.75.
Fractional Part Function
Fractional Part Function, often denoted as {x}, represents the decimal part of a real number x after removing its integer part. In simpler terms, it captures the fractional portion of a number, excluding the whole number component. The fractional part function is particularly useful in various mathematical contexts, such as number theory, analysis, and computer science, where understanding the non-integer portion of a number is essential.
In this article, we will learn about the various concepts related to the fractional part function, like the meaning and definition of the fractional part function, properties of the fractional part function, its formula, application, graph, and solved examples for better understanding.
Table of Content
- What is the Fractional Part Function?
- Properties of Fractional Part Function
- Fractional Part Function Formula
- Fractional Part Function Graph
- Fractional Part Function Domain and Range
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