As per screen shots, the apostrophe is only visible in the address bar, it is not visible in the cell. It can be ignored.That's what you can see in the second image. No apostrophe in the formula bar.
How can I make it leave that entire number in place
The 9.9502E+17 is showing the number in exponential format. This means that it is an extremely large number so Excel has formatted it to fit in the column. That example would be the same as 9.9502 x 10^17 or 995020000000000000