Number Theory

# Rational Numbers: Level 2 Challenges

What is $$0.1212 \ldots$$ in fractional form?

If $$\frac{1}{21}$$ equals the repeating decimal $$0.0476190476190...$$, what is the $$51^{st}$$digit after the decimal point of the repeating decimal?

$\frac{n}{ 810} = 0.\overline{d25} = 0.d25d25d25d25\ldots$

For which positive integer $$n$$, will $$d$$ be a digit?

$\large \displaystyle {0. \overline{42}-0.\overline{35}= \, ?}$


Note: $$0.\overline{ab}=0.abababab \ldots$$

Is $$0.285714285714\overline {285714}$$ rational?


Note: The notation $$“\, \overline{285714}"$$ indicates that these digits in the decimal are being repeated. For example, $$0.1\overline{2} = 0.12222 \ldots.$$

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