Question

The order of the set of rational numbers $-4\frac{3}{5}, -3\frac{2}{5}, -4.65, -4.09$from least to greatest.

Short answer

The correct order of rational numbers from least to greatest is $-4.65, -4\frac{3}{5}, -4.09, -3\frac{2}{5}$.

Step-by-step solution

Step 1.

The set of rational numbers $-4\frac{3}{5},-3\frac{2}{5},-4.65,-4.09$.

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 $-4\frac{3}{5},-3\frac{2}{5},-4.65,-4.09$.”

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, $4\frac{3}{5}$will be written as,

$4\frac{3}{5}=\frac{\left(4\times 5\right)+3}{5}$

$4\frac{3}{5}=\frac{23}{5}$

And, $3\frac{2}{5}$will be written as,

$3\frac{2}{5}=\frac{\left(3\times 5\right)+2}{5}$

$3\frac{2}{5}=\frac{17}{5}$

Step 4. Rewrite.

Now, convert $\frac{23}{5}$and $\frac{17}{5}$into decimal notation and then compare the set of rational numbers.

Decimal notation for $\frac{23}{5}$is 4.6.

Decimal notation for $\frac{17}{5}$is 3.4.

Thus, the set of rational number $-4\frac{3}{5},-3\frac{2}{5},-4.65,-4.09$becomes $-4.6,-3.4,-4.65,-4.09$.

Step 5. Arrangement.

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

$\begin{array}{l}-4.65<-4.6<-4.09<-3.4\\ -4.65<-4\frac{3}{5}<-4.09<-3\frac{2}{5}\end{array}$

Hence, the correct order of rational numbers from least to greatest is $-4.65<-4\frac{3}{5}<-4.09<-3\frac{2}{5}$.