The highest number in base 2 you can cram in 40bits is roughly 0.34 * 10^39. I shifted it so the exponent is equal to the number of digits we can fit. 128 bit

The highest number in base 2 you can cram in 40bits is roughly 0.34 * 10^39. I shifted it so the exponent is equal to the number of digits we can fit. 128 bits could indeed only fit the first 39 digits of PI. And even then you haven't really stored PI, because you haven't stored where the comma is supposed to go.