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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The text contains a mathematical question asking for a rational number and an irrational number between 1/3 and 1/2, followed by a solution that provides the answer.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
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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The text contains a mathematical question asking for a rational number and an irrational number between 1/3 and 1/2, followed by a solution that provides the answer.

TYPE: SINGLE_QUESTION_WITH_ANSWER