text: Question
  
  # Insert a rational number and an irrational number between the following:$$\dfrac {1}{3}$$ and $$\dfrac {1}{2}$$.
  
  Solution
  
  ## $$\dfrac {1}{3} = \dfrac {1}{3} \times \dfrac {4}{4} = \dfrac {4}{12}$$ and $$\dfrac {1}{2} = \dfrac {1}{2}\times \dfrac {6}{6} = \dfrac {6}{12}$$Now, $$\dfrac {5}{12}$$ is a rational number between $$\dfrac {4}{12}$$ and $$\dfrac {6}{12}$$. So, $$\dfrac {5}{12}$$ is a rational number lying between $$\dfrac {1}{3}$$ and $$\dfrac {1}{2}$$.Again, $$\dfrac {1}{2} = 0.33333...$$ and $$\dfrac {1}{2} = 0.5$$.Now, $$0.414114111...$$ is a non-terminating and non-recurring decimal.Hence, $$0.414114111...$$ is an irrational number lying between $$\dfrac {1}{3}$$ and $$\dfrac {1}{2}$$.Maths
  
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explanation: The document contains a math question and its corresponding solution. The question asks for a rational number and an irrational number between \(\frac{1}{3}\) and \(\frac{1}{2}\). The solution provides a detailed step-by-step process to find these numbers.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: Question
  
  # Insert a rational number and an irrational number between the following:$$\dfrac {1}{3}$$ and $$\dfrac {1}{2}$$.
  
  Solution
  
  ## $$\dfrac {1}{3} = \dfrac {1}{3} \times \dfrac {4}{4} = \dfrac {4}{12}$$ and $$\dfrac {1}{2} = \dfrac {1}{2}\times \dfrac {6}{6} = \dfrac {6}{12}$$Now, $$\dfrac {5}{12}$$ is a rational number between $$\dfrac {4}{12}$$ and $$\dfrac {6}{12}$$. So, $$\dfrac {5}{12}$$ is a rational number lying between $$\dfrac {1}{3}$$ and $$\dfrac {1}{2}$$.Again, $$\dfrac {1}{2} = 0.33333...$$ and $$\dfrac {1}{2} = 0.5$$.Now, $$0.414114111...$$ is a non-terminating and non-recurring decimal.Hence, $$0.414114111...$$ is an irrational number lying between $$\dfrac {1}{3}$$ and $$\dfrac {1}{2}$$.Maths
  
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distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a math question and its corresponding solution. The question asks for a rational number and an irrational number between \(\frac{1}{3}\) and \(\frac{1}{2}\). The solution provides a detailed step-by-step process to find these numbers.
  
  Label: question-and-answer