Real numbers are an important part of mathematics. Learning this topic will help you to know more about different types of numbers. To understand different types of numbers in maths.
Do you know real numbers are numbers that include:
- Whole number (0,1,2,3,4)
- Rational Numbers (⅓, 0.25)
- Irrational Numbers ( , , etc)
Note: Real numbers can be positive, negative, or zero. Real numbers are considered real because they do not include any imaginary numbers like 4i.
What Real Numbers Do Not Include?
Real numbers do not include:
- Imaginary numbers like , ( The square root of negative numbers are not considered real numbers).
- Infinity is not considered a real number.
Real Numbers on Number Line
On a real number line, a point marked with 0 is represented as the origin. All numbers that lie on the right side of the origin are positive whereas the numbers that lie on the right side of the origin are negative.
If the distance chosen in the number line is 1, then the positive numbers are marked (0,1,2,3, etc) whereas negative numbers are marked as (-1,-2,-3,-4, etc).
Remember, on the number line any point is a real number. For example,
- The number can be 4, 5, 6,7 etc.
- Or rational number like ½
- Or Irrational number like
Real Number Can Have Any Number of Digits
Real numbers can have an infinite number of digits on either side of the decimal points. For example:
- 12345
- 5554
- 000 000 000 4
There can be an infinite number of digits in real numbers after the decimal point. For example: ½ = 0.555
What are the Basic Properties of Real Numbers?
Real numbers are just like other numbers that we widely used. We can add, subtract, multiply, and divide real numbers. The order of addition and multiplication in real numbers does not matter the most, as it holds the commutative property. As a real number does not have an order, if two numbers such as a and b are given, then only one of the following conditions is true:
a = b, a > b, or a < b
Learn Two Important Theorems of Alternate Exterior Angles
Let’s know what alternate exterior angles mean in mathematics. Alternate exterior angles are pairs of angles on the outer side of the parallel lines but located on the opposite side of transversals. Alternate exterior angles are congruent. It implies that they have equal measure.
What are Alternate Exterior Angles?
Alternate exterior angles are angles that are formed when a transversal line passes through two parallel lines. The pair of angles that are formed outside the two parallel lines but on either side of the transversal line is termed alternate exterior angles. Parallel lines are the lines that are equidistant from each other but never meet. When a transversal line passes through two parallel lines, then lies some special properties about the angles that are formed. These properties do not occur if lines are not parallel.
Alternate Exterior Angles Relationship: Parallel and Non-Parallel Case
- In the case of Parallel Line: When a transversal line is cut across the parallel line then the alternate interior angles that are formed have equal measure.
- In the Case of Non-Parallel Lines: When a transversal line is cut across the non-parallel line then the alternate interior angles that are formed have no relationship with each other. All it means is that each angle is simply an alternate angle to other angles.
Alternate Exterior Angles Theorem
Theorem 1:
The alternate exterior angle theorem states that when a transversal line is cut across a parallel line then the alternate exterior angles that are formed are always congruent.
Theorem 2: Converse of Alternate Exterior Angles Theorem
If two lines are cut by a transversal line and the alternate exterior angles that are formed are congruent, then the two lines on which alternate exterior angles are formed are always parallel. CueMaths for more information.
Hope you have found the above information on alternate exterior angles and real numbers beneficial. To know more about these topics, visit Cuemath.
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