Table of Contents

## Can an irrational number be periodic?

Irrational numbers have decimal expansions that neither terminate nor become periodic.

## How do we know irrational numbers don’t repeat?

The digits of pi never repeat because it can be proven that π is an irrational number and irrational numbers don’t repeat forever. . But this string of numbers includes all of the prime numbers (other than 2) in the denominator, and since there are an infinite number of primes, there should be no common denominator.

**How can you identify an irrational number?**

An irrational number is a number that cannot be written as the ratio of two integers. Its decimal form does not stop and does not repeat.

**When a number is periodic?**

Expression used to refer to a number whose decimal notation is repeating. It includes rational numbers where the decimal expansion does not have 0 or 9 as a period.

### Can irrational numbers be repeated?

An irrational number is a number that is NOT rational. It cannot be expressed as a fraction with integer values in the numerator and denominator. When an irrational number is expressed in decimal form, Its decimal value goes on forever, and does not repeat.

### How do you know if it’s irrational or rational?

Answer: If a number can be written or can be converted to p/q form, where p and q are integers and q is a non-zero number, then it is said to be rational and if it cannot be written in this form, then it is irrational.

**How do you know if a series is periodic?**

A sequence is called periodic if it repeats itself over and over again at regular intervals. Formally, a sequence u1, u2, … is periodic with period T (where T>0) if un+T=un for all n≥1. The smallest such T is called the least period (or often just “the period”) of the sequence.

**How do you find the periodic sequence?**

A periodic sequence can be thought of as the discrete version of a periodic function. In particular, for a periodic sequence {an}, there exists a positive integer constant p such that for all n in thhe natural numbers, an=an+p. The constant p is said to be the period of the sequence.

#### How do we know that irrational numbers never repeat?

We know that irrational numbers never repeat by combining the following two facts: every rational number has a repeating decimal expansion, and every number which has a repeating decimal expansion is rational. Together these facts show that a number is rational if and only if it has a repeating decimal expansion.

#### How do you know if a number is rational or irrational?

Cannot Be Written as a Fraction It is irrational because it cannot be written as a ratio (or fraction), not because it is crazy! So we can tell if it is Rational or Irrational by trying to write the number as a simple fraction.

**Why is 22/7 an irrational number?**

The popular approximation of 22/7 = 3.1428571428571… is close but not accurate. Another clue is that the decimal goes on forever without repeating. Cannot Be Written as a Fraction It is irrational because it cannot be written as a ratio (or fraction),

**What is the final product of two irrational numbers?**

The addition or the multiplication of two irrational numbers may be rational; for example, √2. √2 = 2. Here, √2 is an irrational number. If it is multiplied twice, then the final product obtained is a rational number. (i.e) 2. The set of irrational numbers is not closed under the multiplication process, unlike the set of rational numbers.