Question

Given the examples of ratial number​

Answer 1

Answer:

All the natural numbers, whole numbers, integers and fractions are collectively known as rational numbers.

For example

$2 \\ - 1 \\ 1$

1/5

-4/7etc

Answer 2

What is a Rational number?

Do you know from where the word "Rational" originated?

It was originated from the word "ratio". So, rational numbers are very well related to the ratio concept of a ratio.

Rational Numbers Definition:

A rational number is a number that is of the form p/q where p and q integers and q is not equal to 0. The set of rational numbers is denoted by Q.

In other words, If a number can be expressed as a fraction where both the numerator and the denominator are integers, the number is a rational number.

Examples:

If a number can be expressed as a fraction where both the numerator and the denominator are integers, the number is a rational number. Some examples of rational numbers are:

1/2

-3/4

0.3 or 3/10

-0.7 or -7/10

0.141414... or 14/99

Types of rational numbers:

There are different types of rational numbers. We shouldn't assume that only fractions with integers are rational numbers. The different types of rational numbers are:

integers like -2, 0, 3 etc.

fractions whose numerators and denominators are integers like 3/7, -6/5, etc.

terminating decimals like 0.35, 0.7116, 0.9768, etc.

non-terminating decimals with some repeating patterns (after the decimal point) such as 0.333..., 0.141414..., etc. These are popularly known as non-terminating repeating decimals.

How to identify a rational number?

In each of the above cases, the number can be expressed as a fraction of integers. Hence, each of these numbers is a rational number. To find whether a given number is a rational number, we can check whether it matches with any of these conditions:

We can represent the given number as a fraction of integers

We the decimal expansion of the number is terminating or non-terminating repeating.

All whole numbers are rational numbers

Example: Is 0.923076923076923076923076923076... a rational number?

Solution:

The given number has a set of decimals 923076 which is repeating continuously.

Rational Numbers in decimal form:

Rational numbers can also be expressed in decimal form. Do you know 1.1 is a rational number? Yes, it is because 1.1 can be written as 1.1= 11/10. Now let's talk about non-terminating decimals such as 0.333. Since 0.333... can be written as 1/3, therefore it is a rational number. Therefore, non-terminating decimals having repeated numbers after the decimal point are also rational numbers.

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