Class 9 Exam > Class 9 Questions > Between 3 and 4 there area)10,000 rational nu...
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Between 3 and 4 there are
- a)10,000 rational numbers
- b)1000 rational numbers
- c)Infinitely many rational numbers
- d)500 rational numbers
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Between 3 and 4 there area)10,000 rational numbersb)1000 rational numb...
There is no single number between 3 and 4, there is an infinite amount of numbers. If you are asking for INTEGERS, there are none. If not, you can have unlimited numbers between 3 and 4. For example, a number could be 3.0000000000000000005 or 3.9999999999999997.
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Community Answer
Between 3 and 4 there area)10,000 rational numbersb)1000 rational numb...
Explanation:
There are infinitely many rational numbers between any two rational numbers.
Proof:
Let's take two rational numbers, a and b, where a < b.="" we="" need="" to="" prove="" that="" there="" are="" infinitely="" many="" rational="" numbers="" between="" a="" and="" />
Step 1: Find the difference between a and b.
Let's say d = b - a.
Step 2: Find a rational number, c, such that 0 < c="" />< />
We can take c = 1/10, for example.
Step 3: Multiply d by c.
Let's say m = d * c.
Step 4: Find the smallest positive integer n such that n > 1/m.
We can take n = 1/0.001 = 1000.
Step 5: Divide d by n and add a.
Let's say the result is r. We have:
r = a + (d/n) = a + (d*c*n/n) = a + (d*c) = a + (b-a) * (1/10) = 0.1a + 0.9b
r is a rational number between a and b.
Step 6: Repeat steps 4 and 5 with m/10, m/100, m/1000, and so on.
We can keep finding new rational numbers between a and b by repeating steps 4 and 5 with smaller and smaller values of m.
Conclusion:
There are infinitely many rational numbers between any two rational numbers. Therefore, there are infinitely many rational numbers between 3 and 4.
There are infinitely many rational numbers between any two rational numbers.
Proof:
Let's take two rational numbers, a and b, where a < b.="" we="" need="" to="" prove="" that="" there="" are="" infinitely="" many="" rational="" numbers="" between="" a="" and="" />
Step 1: Find the difference between a and b.
Let's say d = b - a.
Step 2: Find a rational number, c, such that 0 < c="" />< />
We can take c = 1/10, for example.
Step 3: Multiply d by c.
Let's say m = d * c.
Step 4: Find the smallest positive integer n such that n > 1/m.
We can take n = 1/0.001 = 1000.
Step 5: Divide d by n and add a.
Let's say the result is r. We have:
r = a + (d/n) = a + (d*c*n/n) = a + (d*c) = a + (b-a) * (1/10) = 0.1a + 0.9b
r is a rational number between a and b.
Step 6: Repeat steps 4 and 5 with m/10, m/100, m/1000, and so on.
We can keep finding new rational numbers between a and b by repeating steps 4 and 5 with smaller and smaller values of m.
Conclusion:
There are infinitely many rational numbers between any two rational numbers. Therefore, there are infinitely many rational numbers between 3 and 4.
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Between 3 and 4 there area)10,000 rational numbersb)1000 rational numbersc)Infinitely many rational numbersd)500 rational numbersCorrect answer is option 'C'. Can you explain this answer? for Class 9 2026 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Between 3 and 4 there area)10,000 rational numbersb)1000 rational numbersc)Infinitely many rational numbersd)500 rational numbersCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 9 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Between 3 and 4 there area)10,000 rational numbersb)1000 rational numbersc)Infinitely many rational numbersd)500 rational numbersCorrect answer is option 'C'. Can you explain this answer?.
Between 3 and 4 there area)10,000 rational numbersb)1000 rational numbersc)Infinitely many rational numbersd)500 rational numbersCorrect answer is option 'C'. Can you explain this answer? for Class 9 2026 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Between 3 and 4 there area)10,000 rational numbersb)1000 rational numbersc)Infinitely many rational numbersd)500 rational numbersCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 9 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Between 3 and 4 there area)10,000 rational numbersb)1000 rational numbersc)Infinitely many rational numbersd)500 rational numbersCorrect answer is option 'C'. Can you explain this answer?.
Solutions for Between 3 and 4 there area)10,000 rational numbersb)1000 rational numbersc)Infinitely many rational numbersd)500 rational numbersCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 9.
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