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Here's something you can do without thinking, assuming you've had the same realisation I've just had:

Write down a multiple of 2¹⁰⁰

@mur2501 I should have specified: write down a number as a sequence of digits

@christianp

That's fucking long

@christianp My first thought was \( 2^{101} \), my second thought was probably what you're thinking. An interested starting place to create a possibly interesting puzzle.

CC: @mur2501

@ColinTheMathmo @christianp

Also show me what you two are thinking

Answer

Answer

@jsiehler straight in with the trivial answer. Love it!

Answer

@christianp getting straight in with the trivial answer is my career

other more different answer

@christianp For the record, I also see a nonzero answer. I often teach how to recognize which rational numbers have terminating decimal expansions – and if you wanted to show that 1 / \(2^{100}\) terminates in decimal, this trick it a good way to do it.

@christianp how about (5^100)*(2^100) = 10*100 == googol

How about √Pi ? It's irrational! Hahaha!

@christianp Now write down a multiple of 10^(10^100)

hint

@christianp Took me a second.

If anybody is looking for a hint, a multiple of 5¹⁰⁰ is another easy one.

𝓓𝓸𝓷 𝓟𝓲𝓪𝓷𝓸@mur2501@qoto.org@christianp

2^101