Chapter 0.4, Problem 10E

To determine

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

Answer to Problem 10E

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

Explanation of Solution

Given information:

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

Formula used:

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

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

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

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,

  $\begin{array}{l}4\frac{3}{5}=\frac{\left(4\times 5\right)+3}{5}\\ 4\frac{3}{5}=\frac{23}{5}\end{array}$

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

  $\begin{array}{l}3\frac{2}{5}=\frac{\left(3\times 5\right)+2}{5}\\ 3\frac{2}{5}=\frac{17}{5}\end{array}$

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 $-4.6,-3.4,-4.65,-4.09$ .

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