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Find three different irrational number between the rational number 6/7 and 9/11?
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Find three different irrational number between the rational number 6/7...
Three Irrational Numbers Between 6/7 and 9/11
Before we begin, let's first understand what is an irrational number. An irrational number is a number that cannot be expressed as a fraction and has an infinite number of non-repeating decimal places. Examples of irrational numbers include pi, the square root of 2, and the golden ratio.
Method 1: Using Decimal Expansion
One way to find irrational numbers between two rational numbers is to look at their decimal expansion. We can start by converting 6/7 and 9/11 into decimals:
- 6/7 = 0.8571428571...
- 9/11 = 0.8181818181...
From this, we can see that the first digit after the decimal point for 6/7 is 8 and for 9/11 is 8. We can use this information to construct irrational numbers between them:
- 0.8588888888...
- 0.8577777777...
- 0.8571616161...
Each of these numbers is irrational because they have an infinite number of non-repeating decimal places and cannot be expressed as a fraction.
Method 2: Using Square Roots
Another way to find irrational numbers between two rational numbers is to use square roots. We can start by finding the square roots of 6/7 and 9/11:
- sqrt(6/7) = 0.883...
- sqrt(9/11) = 0.878...
From this, we can construct irrational numbers between them by adding or subtracting an irrational number:
- 0.883 - sqrt(2) = 0.174...
- 0.878 + sqrt(3) = 1.408...
- 0.883 - sqrt(5) = 0.352...
Each of these numbers is irrational because they involve adding or subtracting an irrational number to a rational number.
Method 3: Using Pi
We can also use pi to find irrational numbers between two rational numbers. We can start by finding the value of pi:
- pi = 3.1415926535...
We can then use pi to construct irrational numbers between 6/7 and 9/11:
- 6/7 + pi/10 = 1.420...
- 9/11 - pi/100 = 0.817...
- 6/7 + pi/1000 = 0.858...
Each of these numbers is irrational because they involve adding or subtracting pi to a rational number.
Conclusion
Community Answer
Find three different irrational number between the rational number 6/7...
Use formula a+b/2
where a and b are national numbers
There Are infinte rational numbers between two rational numbers.
where a and b are national numbers
There Are infinte rational numbers between two rational numbers.
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Find three different irrational number between the rational number 6/7 and 9/11?
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Find three different irrational number between the rational number 6/7 and 9/11? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Find three different irrational number between the rational number 6/7 and 9/11? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find three different irrational number between the rational number 6/7 and 9/11?.
Find three different irrational number between the rational number 6/7 and 9/11? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Find three different irrational number between the rational number 6/7 and 9/11? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find three different irrational number between the rational number 6/7 and 9/11?.
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