Is the difference of a rational number and an irrational number always irrational? explain?

Differences Between Rational and Irrational Numbers

The difference between rational and irrational numbers can be drawn clearly on the following grounds

1.Rational Number is defined as the number which can be written in a ratio of two integers. An irrational number is a number which cannot be expressed in a ratio of two integers.

2.In rational numbers, both numerator and denominator are whole numbers, where the denominator is not equal to zero. While an irrational number cannot be written in a fraction.

3.The rational number includes numbers that are perfect squares like 9, 16, 25 and so on. On the other hand, an irrational number includes surds like 2, 3, 5, etc.

4.The rational number includes only those decimals, which are finite and repeating. Conversely, irrational numbers include those numbers whose decimal expansion is infinite, non-repetitive and shows no pattern.

After reviewing the above points, it is quite clear that the expression of rational numbers can be possible in both fraction and decimal form. On the contrary, an irrational number can only be presented in decimal form but not in a fraction. All integers are rational numbers, but all non-integers are not irrational numbers.

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