Which set of numbers is correctly ordered from greatest to least?
Accepted Solution
A:
Answer:Step-by-step explanation:Given numbers: [tex]7\tfrac{1}{3}\,,\,\frac{221}{30}\,,\,7.\overline{36}\,,\,16\sqrt{2e}[/tex]We need to arrange these numbers from greatest to least .On writing these numbers in simplified form, we get [tex]7\tfrac{1}{3}=\frac{22}{3}=7.33\\\frac{221}{30}=7.367\\7.\overline{36}=7.3636...\\16\sqrt{2e}=16\times \sqrt{5.437}=16\times 2.332=37.312[/tex]Here,[tex]7.\overline{36}[/tex] has a non-terminating repeating decimal expansion .Vale of e = 2.718[tex]16\sqrt{2e}\,,\,\frac{221}{30}\,,\,7.\overline{36}\,,\,7\tfrac{1}{3}[/tex]The greatest number is [tex]16\sqrt{2e}[/tex]Then number less than [tex]16\sqrt{2e}[/tex] is [tex]\frac{221}{30}[/tex]Then number less than [tex]\frac{221}{30}[/tex] is [tex]7.\overline{36}[/tex]Then number less than [tex]7.\overline{36}[/tex] is [tex]7\tfrac{1}{3}[/tex]i.e [tex]16\sqrt{2e}\,,\,\frac{221}{30}\,,\,7.\overline{36}\,,\,7\tfrac{1}{3}[/tex]So, answer is option 4.