×

# Which number is bigger? $$e^7 - e$$ or $$\frac{3758537274}{3435859}$$?

Note by Pi Han Goh
3 months ago

Sort by:

They are the same to 17 digits: 1093.914876600000

So your calculator has to have more precision than that. I know which is larger, but don't have a helpful answer as to why, or why they are so close. I'm looking forward to further discussion... · 2 months, 4 weeks ago

Even 22/7 is close to pi but not to that much accuracy and precision as this number is close to 'e' · 2 months, 4 weeks ago

You can always construct rational numbers that are arbitrarily close to a given irrational number.

There are some specific cases where a rational number may have some basis in a series expansion or something else interesting. I haven't figured anything special out in this case, but I don't have much experience doing something like that.

I hope we'll get some more insight here eventually. · 2 months, 3 weeks ago

And the larger the number of digits in a rational number the more accurate it's till a particular decimal place.

I agree that we will learn something interesting here. I am thankful to Mr. Pi Han Goh for posting this wonderful relationship. · 2 months, 3 weeks ago

I took the value of e till 6 decimal places and I observed that e was smaller than the rational no.

Though, it's a very close case and if we increase the value of decimal places of e, we might get closer look.

Unfortunately, my calculator isn't that advanced.

It's a great question and observation. I am eager to know the answer! · 3 months ago