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Teacherbot 03 Sep, 02:26:22

Sure! Here are some examples of rational approximations for irrational numbers:

1. π (pi): A common rational approximation for pi is 22/7, which is equal to approximately 3.142857. Another commonly used approximation is 355/113, which is equal to approximately 3.141593.

2. √2 (square root of 2): A rational approximation for the square root of 2 is 3/2, which is equal to 1.5. Another approximation is 7/5, which is equal to 1.4.

3. √3 (square root of 3): A rational approximation for the square root of 3 is 265/153, which is equal to approximately 1.732026. Another approximation is 19/11, which is equal to approximately 1.727273.

4. e (Euler’s number): A rational approximation for Euler’s number is 87/32, which is equal to approximately 2.71875. Another approximation is 193/71, which is equal to approximately 2.71831.

These are just a few examples, and there are many more rational approximations for irrational numbers depending on the level of precision required.

You 03 Sep, 02:27:45

Make this simpler to understand

Teacherbot 03 Sep, 02:27:45

Certainly! Here are some simplified rational approximations for irrational numbers:

1. π (pi): A commonly used approximation for pi is 22/7, which is approximately 3.14. Another approximation is 355/113, which is approximately 3.14 as well.

2. √2 (square root of 2): A simple approximation for the square root of 2 is 3/2, which is equal to 1.5. Another approximation is 7/5, which is equal to 1.4.

3. √3 (square root of 3): A simplified approximation for the square root of 3 is 265/153, which is approximately 1.73. Another approximation is 19/11, which is approximately 1.73 as well.

4. e (Euler’s number): A simplified approximation for Euler’s number is 87/32, which is approximately 2.72. Another approximation is 193/71, which is approximately 2.71.

These simplified rational approximations give a good estimate of the values of these irrational numbers without getting into too much detail.