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Number Theory

Rational Numbers

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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