Inspired by this Monty Python skit...

Escape from the Castle of Exaggeration

Having escaped from your cell in the castle, you find the exit door which leads to freedom. The door is protected by a keypad lock.

A guard, Alice, approaches from one end of the corridor.

"Can I help you?" says Alice.
"What number do I need to type to open this door?" you ask.
"5760."
"Thanks."

As Alice walks off, you think "that was surprisingly easy..."

You type in 5760. The door doesn't open. Instead, the display reads: Incorrect. Two attempts remaining.

Another guard, Bob, approaches from the other end of the corridor.

"Can I help you?" he asks.
"I was told the code for this door is 5760, but it's not working."
"What? That's not the code," says Bob. Then he suddenly groans and rolls his eyes.
"Oh, I know what's happened," he says wearily. "You've been speaking to that idiot Alice, haven't you? The thing is, she's a habitual exaggerator of numbers. Still, at least she's consistent. Every number Alice says is exactly 4 times the number she means."

Bob walks off. You type 1440 onto the keypad. The display reads: Incorrect. One attempt remaining. Below this is an additional message: WARNING: a further incorrect attempt will result in the user being dropped into a bottomless pit."

You realise you are standing on a trapdoor, which up until now had escaped your attention. You also notice the black and yellow hazard tape surrounding it, on which is printed "ENTRANCE TO PIT (warning: bottomless)".

Alice comes patrolling up the corridor again.

"Is it true you're a habitual exaggerator of numbers?" you ask.
"Yes," says Alice.
"So every number you say is 4 times the number you mean?"
"What? No, that's not right," says Alice. "Oh, wait... have you been talking to that blundering cretin Bob?"
"Yes."
Alice nods. "Ah, well, that explains it. He's a habitual under-exaggerator of numbers. Whenever Bob says a number, you have to multiply it by 36 to get the number he means."
"Right..."

Alice turns round and marches back down the corridor out of sight.

Both guards always tell the truth, apart from their consistent and linear scaling of any number they say. You do not know how many digits are in the code. There is a decimal point on the keypad, so it might not even be an integer. There is no minus sign, so you can assume the answer is not negative.

You have one attempt left at the code, so think carefully.... what is it?