Which of the following points lie in the solution set to the following system of inequalities? (1 point)
1 answer:
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Option B
-0.249851765 is a irrational number
<em><u>Solution:</u></em>
Given number is -0.249851765
We have to classify the number
Let us first understand about irrational, real, whole, integer and rational numbers
<h3><u>Integers:</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.
Thus -0.249851765 has non zero digits after decimal point. So it is not a integer
<h3><u>Whole numbers:</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 -0.249851765 is negative number. So it is not a whole number
<h3><u>Natural numbers:</u></h3>A natural number is an integer greater than 0. Natural numbers begin at 1 and increment to infinity: 1, 2, 3, 4, 5, etc. Natural numbers are also called "counting numbers" because they are used for counting.
A decimal is a natural number if it is non-negative and the only digits after its decimal points are zero
So the given number -0.249851765 is a negative number and so it is not a natural number
<h3><u>Rational numbers:</u></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.
The rational numbers includes all positive numbers, negative numbers and zero that can be written as a ratio (fraction) of one number over another.
When a rational number fraction is divided to form a decimal value, it becomes a terminating or repeating decimal.
So -0.249851765 is not a rational number
<h3><u>Irrational number:</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
So the given number -0.249851765 is irrational number
We can conclude that:
-0.249851765 is a irrational number, So Option B is correct