Number Theory

Rational Numbers

Converting Repeating Decimals into Fractions

         

Which of the following is equal to 119\frac{11}{9}?

A) 1.11.1
B) 1.11.\overline{1}
C) 1.21.2
D) 1.21.\overline{2}
E) 1.91.9

Details and assumptions:

9.3=9.33333...9.\overline{3} = 9.33333...

0.111111=190.121212= ?\begin{aligned} 0.111111\ldots &= \frac{1}{9} \\ \\ 0.121212\ldots &= \ ? \end{aligned}

Express 1.294 1 . 2 \overline{94} as a fraction.

Evaluate 0.269.7\displaystyle{\frac{ 0 . \overline{26} }{ 9 . \overline{7} }} by changing the decimals into fractions.

Which of the following is equal to 0.210.\overline{21}?

Details and assumptions:

9.3=9.33333...9.\overline{3} = 9.33333...

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