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Is 0 a reasonable number? In short, correctly! But before we define why, let"s discuss what rational and irrational numbers are.

You are watching: Is zero a rational number or irrational number

What are Rational Numbers?

When a rational number is composed as the fraction, a/b, both a and b room integers and b is a non-zero denominator. Come clarify, integers space non-fractional entirety numbers. They can be negative or positive integers that don’t have actually decimal points.

Let’s explain the difference between rational and irrational numbers.

When expressed in the rational expression type of a/b, no a and b deserve to have decimal points. However, the fraction of a reasonable number can be a number that, as soon as not express in the kind of a/b, has decimal points. That can even have an exponential quantity of decimal points. Here are some instances of rational and also irrational numbers:

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Even despite 2.5 is a decimal and also

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is a decimal with significantly repeating numbers, they space rational numbers due to the fact that both of them can be convert to reasonable expressions in the form of a fraction:

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Pi and the square root of 2 room irrational numbers due to the fact that there is no possible way to convert them into a fraction. There room no two integers that have the right to be used in ratio, or fraction form, to express one irrational number.

Why Is 0 a rational Number?

In a reasonable expression, you can’t divide by zero. The denominator should be a non-zero integer. This is because any type of quotient divided by 0 results in a non-integer. The number doing the dividing, however, can it is in zero. Watch the below fraction p/q:

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This reasonable expression proves the 0 is a rational number because any kind of number deserve to be divided by 0 and equal 0.

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Fraction r/s reflects that as soon as 0 is separated by a whole number, it results in infinity. Infinity is not an integer due to the fact that it cannot be to express in fraction form. Thus, it"s one irrational number:

How You’ll use the Answer to ‘Is 0 a reasonable Number?’

Understanding why 0 is a rational number help you know just how integers work and distinguish between rational and also irrational numbers. It also makes it much easier to learn comparable math principles like irrational numbers, natural numbers, and real numbers.