Question 1150774
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The tutor @ikleyn has a great simple approach.


Below is an alternative method.


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Using a calculator, 
5/6 = 0.833
6/7 = 0.857
both are approximate


Pick some decimal value between 0.833 and 0.857, say the number 0.840 which is the same as 0.84


Convert that decimal to a fraction. Reduce.
0.84 = 84/100 = (21*4)/(25*4) = 21/25


The fraction 21/25 is between 5/6 and 6/7


We can write {{{5/6 < 21/25 < 6/7}}} because {{{0.833 < 0.84 < 0.857}}}


Note: there are infinitely many answers because there are infinitely many values between 0.833 and 0.857 assuming you are allowed to go beyond three decimal places. If you restrict yourself to 3 decimal places, then then there aren't infinitely many answers; however, there are still a lot of answers to choose from. 
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