Why does 1-(0.5^50) equal 99% while 0.5^50 = 8.8?

Question

This is a part of another calculation for a different purpose but this is baffling me.

I enter into my calculator ".5^50" and I get a long number roughly equaling 8.8. My formula now has me subtract that amount from 1 which I would logically conclude to be -7.8. This number however isn't the kind of outcome I was expecting. I'm expecting a number between 0 and 1.

So I decided to enter this into a scientific calculator directly. I entered 1-(0.5^50) and I got 0.99; my expected value.

What am I missing here? How does 1-(0.5^50) resolve to the point where it equals 0.99 when 1-8.8 clearly resolves to -7.8?

Answer 1

8.88E-16, not 8.88

Answer 2

Becase 0.5^50 does NOT equal 8.8

it's 8.8817841970012523233890533447266e-16

That's 15 (or 16) zeros before the 8.8

Answer 3

if you think about it, a fraction to a power always gives you a smaller number. for example

(1/2)^2 = 1/4

(1/2)^3 = 1/8



So (1/2)^50 cannot give you 8.8. thats 1/(1.13x10^15)



what it actually gives you (1/2)^50 = 8.88x10^-16.



1 - 8.88x10^-16 is essentially gives you 0.999999999 blah. which is about 1.

Answer 4

0.5⁵⁰ = 8.88178x10⁻¹⁶ (scientific notation)

0.5⁵⁰ = 0.000000000000000888178 (decimal form)



thus,



1 - 0.5⁵⁰ = 1 - 8.88178x10⁻¹⁶



1 - 0.5⁵⁰ = 1 - 0.000000000000000888178



1 - 0.5⁵⁰ = 0.999999999999999111822



1 - 0.5⁵⁰ ≈ 1

Answer 5

0.5^50 is actually 8.88 * 10^(-16) [rounded], not 8.88.



1 - (8.88 * 10^(-16)) = 0.999999999999999112

Answer 6

Oh please. I see a math problem on here everyday yet no one answers them. We are all stupid. Stop wasting your time