Analysis About Real Numbers
The number that is found in the real world is termed a real numbers. All around us, there are numbers. A natural numbers are used to count objects, whereas rational numbers represent fractions. On the other hand, an irrational number would be used to calculate square feet of integers, numbers to measure temperature, and so on. These different types of numbers are a collection of real numbers. Let us have an idea about real numbers and the important properties that they showcase.
More about Real Numbers
Any number that comes to our mind except complex numbers is known as a real no. It includes rational numbers like positive or negative integers, Irrational numbers, and fractions. There are some numbers that cannot be considered to be real numbers. They fall into the category of non -real numbers.
Real Numbers and their Types
It is well known that real numbers is a combination of rational and irrational numbers. There does not exist any form of a number that is not rational or irrational. What it means is that any number that we pick from R has to be rational or irrational.
- Rational numbers- any number that is defined in the form of a fraction p/q is termed as a rational number. The numerator that is present in the fraction is being represented as p whereas the denominator is q. The q may or may not be equal to zero. Even a rational number may be a real number
- Irrational numbers- such numbers cannot be expressed in the form of a fraction p/q where both of them are integers and q is not equal to zero. Even the decimal value is not going to end at a single point.
The Properties of Real Number
Pretty much like the integers or natural numbers a set of real numbers would satisfy the closure and authoritative property.
- Closure property- the feature indicates that the sum and product of a couple of real numbers would always be a real number.
- Distributive property- real no are known to satisfy the distributive property.
- Commutative property- the product or sum of a couple of real numbers would be remaining the same even after you interchange the order of the numbers.
- Associative property- the product or sum of any three real no would remain the same even after regrouping the number of digits that is part of the number.
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The Real Numbers Present on the Number line
The use of a number line is to display numbers as it is represented by a unique point present in a line. Each and every point on the number line would be showcasing a unique real no. To represent the real numbers on a number line you can consider the following steps
- Draw a horizontal line where there has to be an arrow present on both sides. Then the number 0 is to be marked at the center. This number is known as the point of origin
- Then an equal length is to be made on both sides and with a definite scale you need to label it
- The positive numbers are located on the right side of the origin whereas the negative numbers would be on the left side of the origin.
It is necessary to observe the numbers that is present on the number line. It is going to showcase real numbers like 3/2 , 2 , 0 etc.
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Review A Comprehensive Analysis About Real Numbers.