Calculate the Reciprocal

Name: Calculate the Reciprocal
Author: Jürgen Kummer

Calculator for the reciprocal of a decimal fraction. The reciprocal of a number is 1 divided by that number. The larger a number, the smaller its reciprocal fraction and vice versa. It is calculated with decimal fractions, with normal fractions, the numerator and denominator are simply swapped for the reciprocal fraction, so 3/2 is the reciprocal of 2/3.

Example: the reciprocal of four is one fourth, which equals 0.25 as a decimal fraction.

The reciprocal or inverse of any number except zero can be formed. If the number is represented as a common fraction, such as N/D, you can simply swap the numerator and denominator; the reciprocal is then D/N. This is then usually referred to as an inverse fraction. The inverse of a natural number or integer is a rational number. The inverse of a rational number is a rational number, which can also be a integer or natural number. The inverse of an irrational number, on the other hand, is always an irrational number. The inverse of some integers or rational numbers can also be an infinite but recurring decimal fraction; for example, the inverse of 3 is 1/3 = 0.3333333...

The inverse function assigns its inverse 1/x to each real number x. The function f(x)=x maps the numbers onto a number line, which in the case of a function graph is usually drawn obliquely on the plane. The inverse function g(x)=1/x transforms this function into two mirror-symmetric curves that are not connected. The point where they are separated is zero.

This is the graph of f(x)=x (blue) and the inverse function g(x)=1/x (red), drawn with the function graphs plotter. The inverse function comes from the left with very small negative values and plummets toward negative infinity just before zero. Shortly after zero, it shoots down from the direction of positive infinity, then quickly returns to very small, positive values. Only for values between 0 and 1 is it greater than 1; accordingly, for values between 0 and -1, it is less than -1. For all other values, its absolute value is less than 1 (or 1, for x=−1 and x=1).

Last updated on 06/26/2025. Author: Jürgen Kummer

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