rechneronline.de

Decimal Places of Irrational Numbers

Decimal Places of Irrational Numbers | Calculate with Large Numbers | Billion and Milliard | Write Out Powers | Exponential Function

Calculation of up to 2000 decimal places of the transcendental numbers π, e, φ, irrational roots, as well as their their multiples and rational fractions. π is pi, e is Euler's number and φ is the golden ratio.

A multiple for multiplication and division can be entered, 1/1 is preset, also fractions like 1/3 or 0.5 are possible. To calculate a rational number, like 1/7, with arbitrary accuracy, enter this fraction and press 1. If a square root should be calculated, then enter the value after the √-symbol, here 2 is preset. If the from-value is 0, then all places before the decimal point will be shown. If the to-value is empty, 2000 places after the decimal point will be calculated. At from and to, values between 0 and 2000 are allowed. Of course, the to-value must be larger than the from-value. To calculate, press the according button. The calculation might take a while, especially for roots.

Example: the tenth to twentieth decimal place of 2*π is 17958647692.

Irrational, i.e. inaccessible to the mind, are numbers with an infinite number of decimal places that do not repeat regularly. Such numbers are often the roots of rational numbers. Irrational numbers cannot be represented by fractions. A distinction must be made between rational numbers with an infinite number of decimal places that can be written as a fraction, for example one third. As a decimal fraction, this is 0.3333...
Such irrational numbers, which cannot be represented by roots, are called transcendental numbers. These include the number π (pi) and Euler's number e. The ratio of the golden ratio φ (phi), on the other hand, can be represented by a root, namely

( 1 + √5 ) / 2

This page in German: Nachkommastellen irrationaler Zahlen, Rechnen mit großen Zahlen, Billion und Milliarde, Potenzen ausschreiben, Exponentialfunktion