Problem 14

Explanation

Converting to Fractions

To determine the order from smallest to largest, we convert all numbers into fractions with a common denominator.

Finding a Common Denominator

We use $2100$ as the common denominator (LCM of $100$, $14$, and $3$).

For $\sqrt{12}$, since its value is approximately $3.46$, if converted to a fraction over 2100, it would be very large (much larger than the others which are all below 2).

Conclusion

Based on the numerators with the common denominator:

So the order is:

Returning to the original forms: