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How to make the expression 6÷8=27 correct

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#puzzle #decimal-expansion
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Prove the following statements involving repeating decimals

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#fractions #rational-numbers #decimal-expansion
81
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Is it possible to get a number which consists only of digit 1?

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#number-theory #decimal-expansion
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Why is 0.3 to power of 2 0.09 and not 0.9?

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#arithmetic #exponentiation #decimal-expansion
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Is it possible to prove a repeating decimal is infinite

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#fractions #infinity #decimal-expansion
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A number with an interesting property. $abcd=a^b c^d$

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#number-theory #decimal-expansion
290
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Does there exist a fraction whose repeating decimal has a period of some highest number or can the number of this period take infinitely many values?

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#sequences-and-series #algebra-precalculus #elementary-number-theory #decimal-expansion
139
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Do infinitely many primes exist whose decimal string has no consecutive repeated digits?

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#number-theory #prime-numbers #decimal-expansion
576
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Why real numbers doesn't end with infinitely many 9s?

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#real-numbers #decimal-expansion
75
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Digit completeness

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#decimal-expansion
124
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Show that the decimal number obtained by concatenating the digits of n! successively represents an irrational number.

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#decimal-expansion
48
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How do you determine unique pairs of rational ratios of decimals?

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#decimal-expansion
1.9k
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Show that the last two decimal digits of a perfect square must be one of the following pairs.

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#elementary-number-theory #decimal-expansion #square-numbers
454
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Infinite decimal expression of rational numbers

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#divisibility #rational-numbers #decimal-expansion
71
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$E$ is nowhere dense

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#real-analysis #general-topology #real-numbers #decimal-expansion

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