Question

Classify the number 5.923076923076

Answer 1

Option C

5.923076923076 is real and rational number

Solution:

Given number is 5.923076923076

We have to classify the number

Let us first understand about irrational, real, whole, integer and rational numbers

Whole numbers:

Whole numbers are positive numbers, including zero, without any decimal or fractional parts. Negative numbers are not considered "whole numbers."

But the given number 5.923076923076 has decimal part

So it is not a whole number

Real numbers:

Positive or negative, large or small, whole numbers or decimal numbers are all Real Numbers. They are called "Real Numbers" because they are not Imaginary Numbers.

The given number 5.923076923076 has decimal part, so it is real number

Integers:

An integer is a whole number (not a fractional number) that can be positive, negative, or zero. Examples of integers are: -5, 1, 5, 8, 97, and 3,043

Every integer can be expressed as a decimal, but most numbers that can be expressed as a decimal are not integers. If all the digits after the decimal point are zeroes, the number is an integer. If there are any non-zero digits after the decimal point, the number is not an integer.

So the given number 5.923076923076 has non zero digits after decimal point

Thus 5.923076923076 is not a integer

Irrational number:

An irrational number is real number that cannot be expressed as a ratio of two integers.

When an irrational number is expressed in decimal form, it goes on forever without repeating

But the given number 5.923076923076 has repeating digits after decimal point

So it is not a irrational number

Rational number:

A rational number is a number that can be expressed as a fraction (ratio) in the form $\frac{p}{q}$ where p and q are integers and q is not zero.

When a rational number fraction is divided to form a decimal value,  it becomes a terminating or repeating decimal.

But the given number 5.923076923076 has repeating digits after decimal point

5.923076923076 ⇒ $5.923076 \underline{923076}$

So we can clearly observe that 923076 is repeating in decimal point

So the given number is rational number

We can conclude that:

5.923076923076 is real and rational number. Option C is correct