# Tagged Questions

For questions about decimal expansion, both practical and theoretical.

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### Can a change of basis modify irrationality/transcendence?

Fix a real number $x$. We can consider its binary expansion, for instance $x = (0.01101001100101101001011\ldots)_2$. Now we consider the real number $y = (0.01101001100101101001011\ldots)_{10}$ : we ...
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### No square has a decimal expansion ending in 79

Show that no square number has a decimal ending in 79. More generally, find all possible two-digit endings for squares. Let any digit number ending at 79 be represented as $$a_nx^n+.....+7x+9$$ Plug ...
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### Can fractions actually be converted to decimals?

I was working on a spreadsheet in Excel (I'm a plebe, I know), and I came across a fraction that actually equated to 33.3% of a total number. While looking at it, and looking at the number that went ...
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### Is the infinite decimal fraction $1.23456…n$ irrational?

How to prove that the number $1.23456\dots n$ is an irrational number? The number consist, of course, of natural numbers in increasing sequence.
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### Relationship between decimal length and Fibonacci number

There are 6 single digit Fibonacci numbers. For all other number of digits in the decimal system, there are either 4 or 5 Fibonacci numbers. For example, between 10000 and 99999 there are 5: 10946 ...
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### a*b = a/b = b/a (what's this symmetry called?)

I was playing around with numbers the other day, and I found an interesting symmetry, that I would like to know if it has any specific name assigned to it. Let's assume the notation n:a to refer to ...
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### How to prove that every power of 6 ends in 6?

Yesterday I had the traditional math matriculation exam, and in it there was a question "In what digit does the number $2016^{2016}$ end in?" After the test The Matriculation Examination Board ...