Order each set of rational numbers from least to greatest.

$3.8, 3.06, 3\frac{1}{6}, 3\frac{3}{4}$

The set of rational numbers $3.8,3.06,3\frac{1}{6},3\frac{3}{4}$.

Rational numbers are of the form $\frac{p}{q}$ where p and q are integers and $q\ne 0$.

Mixed fractions of the form $m\frac{p}{q}$can be converted into proper fractions as,

$m\frac{p}{q}=\frac{\left(m\times q\right)+p}{q}$

Consider the provided statement “The set of rational numbers $3.8,3.06,3\frac{1}{6},3\frac{3}{4}$.”

Recall that the mixed fractions can be converted into proper fractions as,

$m\frac{p}{q}=\frac{\left(m\times q\right)+p}{q}$

So, $3\frac{1}{6}$will be written as,

$3\frac{1}{6}=\frac{\left(6\times 3\right)+1}{6}$

$3\frac{1}{6}=\frac{19}{6}$

And, $3\frac{3}{4}$will be written as,

$3\frac{3}{4}=\frac{\left(3\times 4\right)+3}{4}$

$3\frac{3}{4}=\frac{15}{4}$

Now, convert $\frac{19}{6}$and $\frac{15}{4}$into decimal notation and then compare the set of rational numbers.

Decimal notation for $\frac{19}{6}$is equivalent to $3.16$.

Decimal notation for $\frac{15}{4}$is 3.75.

Thus, the set of rational number $3.8,3.06,3\frac{1}{6},3\frac{3}{4}$becomes $3.8,3.06,3.16,3.75$.

Now, arrange this set of rational numbers from least to greatest as,

$\begin{array}{l}3.06<3.16<3.75<3.8\\ 3.06<3\frac{1}{6}<3\frac{3}{4}<3.8\end{array}$

Hence, the correct order of rational numbers from least to greatest is $3.06<3\frac{1}{6}<3\frac{3}{4}<3.8$.