〜 ★ dCode presents ★ 〜

Repeating Decimals

Tool to find the period of a fraction or a decimal number with repeating decimals. The period is a set of digits that is repeated at infinity in the decimals of the number (usually a rational number or a periodic fraction).

Recurring Decimal Detection

Fraction Finder

Answers to Questions

What are repeating decimal in a fraction?

The periodic decimal development of a fraction is the sequence of numbers which is repeated at infinity in the decimal writing of the number.

Example: 1/3 = 0.3333333333 ... The digit 3 is repeated to infinity

Example: 1/27 = 0.037037037037037 ... The digits 037 are repeated to infinity

It is better to write the fraction in irreducible form.

Inverses of prime numbers provide interesting periodic decimal developments.

How to write repeating decimal?

Multiple notations are possible.

The first uses ... points of suspension, but does not define the part that repeats. It is practical but not rigorous and therefore not recommended.

Example: \( 37/300 = 0.12333333333 ... \)

Notation with a bar above the repeated part.

Example: \( 37/300 = 0.12 \overline{3} \)

Notation with a bar below the repeated part.

Example: \( 37/300 = 0.12 \underline{3} \)

Notation between brackets

Example: \( 37/300 = 0.12 [3] \)

Source code

dCode retains ownership of the source code of the script Repeating Decimals online. Except explicit open source licence (indicated Creative Commons / free), any algorithm, applet, snippet, software (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt, encrypt, decipher, cipher, decode, code, translate) written in any informatic langauge (PHP, Java, C#, Python, Javascript, Matlab, etc.) which dCode owns rights will not be given for free. To download the online Repeating Decimals script for offline use on PC, iPhone or Android, ask for price quote on contact page !

Questions / Comments

Team dCode likes feedback and relevant comments; to get an answer give an email (not published). It is thanks to you that dCode has the best Repeating Decimals tool. Thank you.

Source : https://www.dcode.fr/number-repeating-decimal