# Can a irrational number be expressed as a fraction?

Table of Contents

## Can a irrational number be expressed as a fraction?

Real Numbers: Irrational Irrational Numbers: Any real number that cannot be written in fraction form is an irrational number. For example, and are rational because and , but and are irrational. All four of these numbers do name points on the number line, but they cannot all be written as integer ratios.

**What can irrational numbers be expressed as?**

Like all real numbers, irrational numbers can be expressed in positional notation, notably as a decimal number. In the case of irrational numbers, the decimal expansion does not terminate, nor end with a repeating sequence.

**What is the difference between fraction and rational number?**

A fraction is any number of the form a/b where both “a” and “b” are whole numbers and b≠0. On the other hand, a rational number is a number which is in the form of p/q where both “p” and “q” are integers and q≠0. Thus, a fraction is written in the form of m/n, where n is not 0 and m & n are whole (or natural numbers).

### Why is pi an irrational number?

Pi is an irrational number, which means that it is a real number that cannot be expressed by a simple fraction. That’s because pi is what mathematicians call an “infinite decimal” — after the decimal point, the digits go on forever and ever. (These rational expressions are only accurate to a couple of decimal places.)

**Why are irrational numbers denoted by S?**

Answer: Irrational numbers are numbers that cannot be expressed as the ratio of two whole numbers. When expressed as a decimal, irrational numbers go on forever after the decimal point and never repeat.

**Why all rational numbers are not fractions?**

Every fraction is a rational number but a rational number need not be a fraction. Since every natural number is an integer. Therefore, a and b are integers. Thus, the fraction a/b is the quotient of two integers such that b ≠ 0.

## Can root 2 be written as a fraction?

Root 2 is an irrational number as it cannot be expressed as a fraction and has an infinite number of decimals. So, the exact value of the root of 2 cannot be determined.

**Is the difference of a rational and irrational number always irrational?**

The sum or difference of a rational number and an irrational number is irrational.

**Can some integers be irrational numbers?**

Pi is an irrational number because it cannot be expressed as a ratio (fraction) of two integers: it has no exact decimal equivalent, although 3.1415926 is good enough for many applications. The square root of 2 is another irrational number that cannot be written as a fraction.

### How do you prove that a number is irrational?

To prove that a number is irrational, show that it is almost rational. Loosely speaking, if you can approximate \\alpha well by rationals, then \\alpha is irrational. This turns out to be a very useful starting point for proofs of irrationality.

**What is the difference between an irrational number and an integer?**

An irrational number is any real number that cannot be expressed as a ratio a/b, where a and b are integers, with b non-zero, and is therefore not a rational number. An integer is any real whole number. Basically, this means that an irrational number cannot be represented as a simple fraction.

**What makes something an irrational number?**

An irrational number is any Real number that cannot be expressed as a ratio of two Integers. A Rational number can be expressed as such a ratio, hence rational. Irrational simply means not rational. The classic example of an Irrational number is [math]\\sqrt2[/math].