Q7. - Algebra 1

Question

Order each set of rational numbers from least to greatest.

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

Step-by-Step Solution

Answer

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

Step 1.

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

Step 2. Formula Used.

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,

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

Step 3. Calculation.

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,

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

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

Step 4. Rewrite.

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 $3.8,3.06,3.16,3.75$.

Step 5. Arrangement.

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 $3.06<3\frac{1}{6}<3\frac{3}{4}<3.8$.