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Is 3.5 a rational or irrational number?

Last Updated : 22 Apr, 2024
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3.5 a Rational Number.

Before moving further it’s important to understand the definitions of rational and irrational numbers.

Rational Numbers Definition

The numbers that can be expressed as a fraction of two integers, where the denominator is not zero are called Rational Numbers. In other words, a number is rational if it can be written in p/q, where p and q are integers and q is not equal to zero.

It can be expressed as p/q, where q ≠0

For example, 5/10 is a rational number because both 5 and 10 are integers, and 10 is not zero, so it qualifies as a rational number.

Irrational Numbers Definition

Numbers that cannot be expressed in fractions or ratios of integers are irrational numbers. It can be written in decimals and has endless non-repeating digits after the decimal point. It is denoted by ‘P’.

For example, the square root of 2 (√2) is an irrational number because it cannot be expressed as a fraction of two integers. Its decimal representation goes on indefinitely without repeating any pattern.

Is 3.5 a Rational or Irrational Number?

To determine whether 3.5 is a rational or irrational number, we need to express it as a fraction. A rational number can be expressed as a ratio of two integers.

Given,

3.5 can be written as 3.5 = 7/2,

We can prove mathematically that 3.5 is a rational number.

Proof:

Let x = 3.5

Multiplying both sides by 2:

2x = 2 × 3.5

2x = 7

Dividing by 2:

x = 7/2

Since 3.5 can be expressed as the fraction 7/2, which is a ratio of two integers, we can conclude that 3.5 is a rational number.


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