Question

fundamental mode of vibration for CH3 molecules and H202 ​

Answer 1

As a good rational approximation for the square root of two, with a reasonably small denominator, the fraction 99/70 (≈ 1.4142857) is sometimes used.

The sequence A002193 in the OEIS consists of the digits in the decimal expansion of the square root of 2, here truncated to 65 decimal places: