List all the numbers from the given set that are, a.natural numbers b.whole numbers c.integers d.rational numbers, e.irrational numbers
{-9,-4/5,0,0.25,�ã3,9.2,�ã100}
a.natural numbers
Numbers that are non-negative integers, such as 1,2,12,201,...
There are two definitions of natural numbers, one that includes 0, and the other one does not. Most high-school definitions include 0.
b.whole numbers
Whole numbers do not have decimals nor fractions. They can be positive, negative, or zero. Examples are -100, -23, 0, 40, 47,1729,...
c.integers
Integers are whole numbers. This term is a more technical term than "whole numbers".
d.rational numbers,
Rational numbers are whole numbers or fractions that can be represented by division of two integers, m/n. Whole numbers can be represented by an integer divided by 1.
Examples: 0, 3, 4/5, 144/17, 355/113, -45/13..., 0.4, 3.̅3 (=10/3),
e.irrational numbers
Irrational numbers are real numbers that are not rational, i.e. real numbers that cannot be represented as a quotient of two integers. Examples are: √2, -√94, π and e.
This should give you a good idea of how to classify numbers. Proceed with the exercise and post your answers for checking if you wish.
Note:
If you are wondering what a real number is:
a real number is a number that is not complex. A complex number includes an imaginary component, i. A real number is a subset of complex numbers, which has the general form a+bi, where a and b are real numbers, and i is the square-root of -1. When b=0, the number becomes a real number.
To determine which numbers from the given set are natural numbers, whole numbers, integers, rational numbers, and irrational numbers, we need to understand the definitions of each type of number.
a. Natural numbers: Natural numbers are positive integers starting from 1 and continuing indefinitely. Natural numbers do not include zero or negative numbers.
b. Whole numbers: Whole numbers include all natural numbers along with zero. Whole numbers do not include negative numbers or fractions.
c. Integers: Integers include all whole numbers along with their negative counterparts. Integers include zero, positive whole numbers, and negative whole numbers. However, integers do not include fractions or decimal numbers.
d. Rational numbers: Rational numbers are numbers that can be expressed as a fraction or a ratio of two integers. Rational numbers include all integers along with fractions and terminating or repeating decimals.
e. Irrational numbers: Irrational numbers are numbers that cannot be expressed as a fraction or a ratio of two integers. Irrational numbers include non-terminating and non-repeating decimals. Some well-known examples of irrational numbers are square roots of non-perfect squares and the mathematical constant π (pi).
Now, let's evaluate each number from the given set based on these definitions:
-9: This number is an integer, as it is a negative whole number.
-4/5: This number is a rational number, as it can be expressed as a fraction.
0: This number is a whole number and an integer. It is not a natural number as it is not positive.
0.25: This number is a rational number, as it can be expressed as a fraction.
�ã3: This number is an irrational number, as it is the square root of a non-perfect square (3 is not a perfect square).
9.2: This number is a rational number, as it can be expressed as a terminating decimal.
�ã100: This number is an irrational number, as it is the square root of a non-perfect square (100 is a perfect square).
So, from the given set, we have:
a. Natural numbers: None.
b. Whole numbers: 0.
c. Integers: -9, 0.
d. Rational numbers: -9, -4/5, 0, 0.25, 9.2.
e. Irrational numbers: �ã3, �ã100.
a. Natural numbers: 0, 3, 9
b. Whole numbers: -9, 0, 3, 9
c. Integers: -9, -4/5, 0, 3, 9
d. Rational numbers: -9, -4/5, 0, 0.25, 3, 9.2
e. Irrational numbers: √3, √100