Show that 0.2353535... = 0.23̄5̄ can be expressed in the form p/q, where p and q are integers and q ≠ 0.

Question

TextConversion of Decimal to Rational FormNCERT Textbook

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The sum of 0.3̄ and 0.4̄ is

Show that 3.142678 is a rational number. In other words, express 3.142678 in the form p/q, where p and q are integers and q ≠ 0.

Show that 0.3333... = 0.3̄ can be expressed in the form p/q, where p and q are integers and q ≠ 0.

Show that 1.272727... = 1.2̄7̄ can be expressed in the form p/q, where p and q are integers and q ≠ 0.

Express the following in the form p/q, where p and q are integers and q ≠ 0.

Express 0.99999 .... in the form p/q. Are you surprised by your answer? With your teacher and classmates discuss why the answer makes sense.