Between a rational and a irrational

In summary, a rational number is a number that can be expressed as a ratio of two integers, while an irrational number cannot be expressed as a ratio of two integers and has an infinite number of non-repeating decimals. These two types of numbers cannot be equal, since a rational number has a finite or repeating decimal representation while an irrational number has an infinite and non-repeating one. Examples of rational numbers include 1/2, 0.75, and 5, while examples of irrational numbers include √2, π, and e. In real life, rational numbers are used in everyday calculations, while irrational numbers are used in fields such as physics and engineering for precise measurements and constants. It is not possible for a number to
  • #1
nerdy_time
1
0
Hello.
Between a rational and a irrational is there a rational? and a irrational? and vice-versa?
I know that between 2 rationals there is a rational and a irrational and that between 2 irrationals there is a rational and a irrational, but i cannot figure this out... please help.
Thanks.
 
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  • #2
Let I be the irrational number and r be the rational number. If I > r, consider the number d = I - r.
 
  • #3
between any two unequal number there is a rational and irrational number. It's easiest to see this in decimal representation.
 

FAQ: Between a rational and a irrational

1. What is the difference between a rational and an irrational number?

A rational number is a number that can be expressed as a ratio of two integers, while an irrational number cannot be expressed as a ratio of two integers and has an infinite number of non-repeating decimals.

2. Can a rational and an irrational number be equal?

No, a rational and an irrational number cannot be equal because a rational number can be expressed as a finite decimal or a repeating decimal, while an irrational number has an infinite number of non-repeating decimals.

3. What are some examples of rational and irrational numbers?

Examples of rational numbers include 1/2, 0.75, and 5. Examples of irrational numbers include √2, π, and e.

4. How are rational and irrational numbers used in real life?

Rational numbers are used in everyday calculations, such as calculating change or measuring ingredients for a recipe. Irrational numbers are used in fields such as physics and engineering to represent precise measurements and constants.

5. Can a number be both rational and irrational?

No, a number cannot be both rational and irrational. A number is either a rational number or an irrational number, but not both at the same time.

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