Question :

What is a ratoinal number and what are the proprties of rational numbers.

Mathematics

Class 8

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2151

Valentina

Aarohi

Rational numbers are represented in the form p/q where q is not equal to zero. It is also a type of real number.. Any fraction with non-zero denominators is a rational number.

The number 1/0, 2/0, 3/0, etc. are not rational, because they give us infinite values but  ‘0’ is a rational number, as we can represent as 0/1, 0/2, 0/3, etc. finally we get again zero.  We can say that any fraction fits under the category of rational numbers, where the denominator and numerator are integers and the denominator is not equal to zero. When the rational number (i.e., fraction) is divided, the result will be in decimal form, which may be either terminating decimal or the repeating decimal.

Thomas

A rational number, in Mathematics, can be defined as any number which can be represented in the form of p/q where q ≠ 0.

### How to identify rational numbers?

To identify if a number is rational or not, we check the conditions. i. e. It is represented in the form of p/q, where q ≠ 0 and the ratio p/q can be further simplified and get the value in a decimal form. The set of rational numbers or numerals are Include positive, negative numbers, and zero and  expressed as a fraction.

Examples of Rational Numbers:

• If p = 10 q = 5,  than p/q = 10/5 = 2 is a rational number.
• If p = 1 and q = 10, than p/q = 1/10 = 0.01 is a rational number.
• if p = 100 and q = 5, than p/q = 100/5 = 20 is a rational number.

## Types of Rational Numbers

A number is rational if we can write it as a fraction, where both denominator and numerator are integers and denominator is a non-zero number.

• Real numbers (R) include all the rational numbers (Q).
• Real numbers include the integers (Z).
• Integers involve natural numbers(N).
• Every whole number is a rational number because every whole number can be expressed as a fraction.
Dashboard

A rational numbers are represented in p/q form where q is not equal to zero. It is also a type of real number. Any fraction with non-zero denominators is a rational number. In rational number, the denominator and numerator are integers and the denominator is not equal to zero.

When the rational number is divided, the result will be in get in decimal form for exampe, 5/2 = 2.5, and 10/3 = 3.3333 etc... (It may be either terminating decimal or the repeating decimal).

Also sometimes, 10/30, 3/9 are rational numbers but when we simplified fuurther we get as 1/3; since common factors between the divisor and dividend is only one. So we when we cancel that number we get a single rational number i.e. 1/3 is in standard form.

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