what is 19/99 rational or irrational ?
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Answers ( 4 )
What is a rational number?
Rational numbers can be represented as a quotient of two whole numbers. They are expressed as an a/b fraction, where a and b are whole numbers and b is non-zero.
Most people have trouble distinguishing between simple fractions and rational numbers. Whole numbers make up fractions, while real numbers make up the numerator and denominator of rational numbers.
What is the difference between rational and irrational numbers?
What are irrational numbers?
Irrational numbers are real numbers that are not rational numbers. Here are some examples of frequently used irrational numbers:
The number (pi) is irrational (Π = 3⋅14159265…), because the decimal value never ends.
√2 is an irrational number. Consider an isosceles equilateral triangle with two sides of equal length, AB and BC. The hypotenuse AC will be √2=1.414213… according to the Pythagorean theorem.
The difference between rational and irrational numbers
Irrational numbers are infinite and non-repeating, while rational numbers are finite and repeating decimals.
Here are some examples of rational numbers:
The number 9 can be expressed as 9/1, 9 and 1 both being whole numbers.
In all trailing decimal forms, 0.5 can be written as 1/2, 5/10, or 10/20.
√81 is a rational number since it can be reduced to 9.
0.7777777 is a rational number with recurring decimals.
Examples of irrational numbers:
The denominator of 5/0 is zero, which makes it an irrational number.
Π is an irrational number, because it is a non-repeating and endless number.
Because it cannot be simplified, the square root of 2 is an irrational number.
Because it does not repeat or end, 0.212112111… is an irrational number.
The ratio of two integers can be used to express rational numbers. Since 19/99 is an expression, we know that 19 and 99 are both integers. Therefore, we can conclude that 19/99 is a rational number because it is expressed as the ratio of two integers. Additionally, 19/99 is equal to 0.191919.
How to Identify Rational Numbers
A rational number can be expressed as a fraction of whole numbers. Therefore, each of these digits is a rational digit. To determine if a number is rational, check if it meets any of the following criteria:
The given number can be represented as a fraction of integers.
It can be determined whether the decimal expansion of the number is terminated or unterminated.
All rational numbers are integers.
The different types of rational numbers
There are different types of rational numbers. However, it should not be assumed that only rational numbers are fractions of whole numbers. Here are the different types of rational numbers:
Positive rational numbers
If the numerator and denominator of a rational number are both positive integers or both negative integers, the number is said to be positive. In other words, if the numerator and the denominator of a rational number have the same sign, it is positive. Positive rational numbers include numbers like 0.2, 6, or 2/5. In this case, 0.2 can be expressed as 1/5 and 6 as 6/1.
Negative rational numbers
If the numerator and the denominator have a different sign (i.e. one is a positive integer and the other a negative integer), the rational number is said to be negative. For example, the following rational numbers are negative: -1/7, -4/5, -25/11, -10/19, -13/23, while the following rational numbers are positive: -11/-14, 2/3, -3/-4, and 1/2.
Real numbers
Real numbers include all rational numbers. A real number is a number that can be found and used in everyday life. Real numbers are used to count things, rational numbers are used to represent fractions, irrational numbers are used to calculate the square root of a number, and whole numbers are used to measure temperature, etc. The set of real numbers is made up of these many kinds of numbers.
Whole numbers
Since every whole number can be written as a fraction, every whole number is a rational number. A set of numbers that includes all positive integers and 0 is called an integer. Whole numbers are fractions, decimals, and negative values that are not real numbers.
Properties of rational numbers
Here are some of the most important properties of rational numbers. Let’s take a closer look at these features while exploring a list of rational numbers.
Algebraic closure property
The algebraic closure property of rational numbers states that two rational numbers added, subtracted, multiplied, or divided all produce a rational number. Let’s see how this property affects all basic arithmetic operations.