Help with math problem
1 answer:
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Option C
5.923076923076 is real and rational number
<em><u>Solution:</u></em>
Given number is 5.923076923076
We have to classify the number
Let us first understand about irrational, real, whole, integer and rational numbers
<h3><u><em>Whole numbers: </em></u></h3>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
<h3><u><em>Real numbers: </em></u></h3>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
<h3><u><em>Integers: </em></u></h3>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
<h3><u><em>Irrational number:</em></u></h3>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
<h3><em><u>Rational number:</u></em></h3>A rational number is a number that can be expressed as a fraction (ratio) in the form 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 ⇒
So we can clearly observe that 923076 is repeating in decimal point
So the given number is rational number
<em><u>We can conclude that:</u></em>
5.923076923076 is real and rational number. Option C is correct