Is my float variable a true random number?

Assume integer below is produced by a true random number generator, and the number changes randomly between 0 and 255.

let integer = 241 // true random number

For the application I'm working on, I need to convert that number into a floating decimal between 0 and 1 to look more like the result from Math.random().

So,

let float = integer/(2**8)-1

Then, for my question, given the initial random number integer am I reducing its randomness if I do this?

let random = float * Math.random() * Math.random() * Math.random()

Note, my purposes for this is not for security, encryption, or cryptography. I just need the added decimal places Math.random() three times adds.