Answer:
Step-by-step explanation:
Here is the corrected question and options:
Option 1:
[tex]7\frac{1}{3} , \frac{221}{30} , 7.36, 3.16\sqrt{2e}[/tex]
Option 2:
[tex]7\frac{1}{3} , 7.36 , \frac{221}{30} , 3.16\sqrt{2e}[/tex]
Option 3:
[tex]3.16\sqrt{2e}, 7.36 , \frac{221}{30} , 7\frac{1}{3}[/tex]
Option 4:
[tex]3.16\sqrt{2e}, \frac{221}{30} , 7.36 , 7\frac{1}{3}[/tex]
Solution:
Lets write each of the above given numbers in a simplified form:
[tex]7\frac{1}{3}[/tex]
Simplify this by converting it into a decimal form:
This becomes:
(3*7+1) / 3 = (21 + 1) / 3 = 22/3 = 7.333333
So
[tex]7\frac{1}{3}[/tex] = 7.3
[tex]\frac{221}{30}[/tex]
Simplify this by converting it into a decimal form:
This becomes:
221/30 = 7.3666666667
So,
[tex]\frac{221}{30}[/tex] = 7.367
[tex]7.36[/tex]
This number comes with a bar sign on .36 which means that the number has a non terminating repeating decimal expansion as 7.3636363636...
So after rounding it off this becomes:
7.36
[tex]3.16\sqrt{2e}[/tex]
Simplify this by converting it into a decimal form:
The value of e = 2.718
This becomes:
3.16 [tex]\sqrt{2*2.718}[/tex]
= 3.16 (√5.436)
= 3.16 * 2.331523
= 7.3679949818
= 7.368
So
[tex]3.16\sqrt{2e}[/tex] = 7.368
7.367995
Now we get the numbers in decimal form:
[tex]7\frac{1}{3}[/tex] = 7.333333 = 7.3
[tex]\frac{221}{30}[/tex] = 7.3666666667 = 7.367
7.36 = 7.3636363636
[tex]3.16\sqrt{2e}[/tex] = 7.3679949818 = 7.368
Now lets order the numbers from greatest to least:
[tex]3.16\sqrt{2e}[/tex]
[tex]\frac{221}{30}[/tex]
7.36
[tex]7\frac{1}{3}[/tex]
So the correct option is:
Option 4
[tex]3.16\sqrt{2e}, \frac{221}{30} , 7.36 , 7\frac{1}{3}[/tex]
