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Find the fraction that equals 0.7266666666... + 0.023333333...

 May 2, 2022
 #1
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Note that \(\dfrac13 = 0.333\dots\) and \(\dfrac23 = 0.666\dots\).

 

Then \(\dfrac1{300} = 0.00333\dots\) and \(\dfrac1{150} = 0.00666\dots\).

 

\(0.72666\dots + 0.02333\dots = 0.72 + 0.02 + 0.00666\dots + 0.00333\dots = 0.74 + \dfrac1{300} + \dfrac1{150}\)

 

I believe you can continue here.

 May 2, 2022

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