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I found these two properties of normal numbers on the Wikipedia page for "normal numbers", but I can't find any other source for them. I was wondering if they were in fact true, and if somebody could give me a hint on how to prove them.

  1. Any number is the product of two absolutely normal numbers.
  2. If $x$ is normal in base $b$, and $q \neq 0$ is a rational number, then $ x\cdot q$ is normal in base $b$.

I was thinking that 1 could sort of follow from Borel's proof that almost every real number is normal. However I'm not sure about the second.

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