Is 3.5 a rational or irrational number?
Last Updated :
22 Apr, 2024
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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