Number Theory

Rational Numbers

Rational Numbers: Level 2 Challenges


What is 0.12120.1212 \ldots in fractional form?

If 121\frac{1}{21} equals the repeating decimal 0.0476190476190...0.0476190476190..., what is the 51st51^{st}digit after the decimal point of the repeating decimal?

n810=0.d25=0.d25d25d25d25 \frac{n}{ 810} = 0.\overline{d25} = 0.d25d25d25d25\ldots

For which positive integer nn, will dd be a digit?

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

Note: 0.ab=0.abababab0.\overline{ab}=0.abababab \ldots

Is 0.2857142857142857140.285714285714\overline {285714} rational?

Note: The notation 285714"“\, \overline{285714}" indicates that these digits in the decimal are being repeated. For example, 0.12=0.12222. 0.1\overline{2} = 0.12222 \ldots.


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