Question

The order of set of rational numbers $2\frac{1}{2},1\frac{7}{8},1.75,2.4$from least to greatest.

Short answer

The correct order of rational numbers from least to greatest is $1.75,1\frac{7}{8},2\frac{1}{4},2.4$.

Step-by-step solution

Step 1.

The set of rational numbers $2\frac{1}{4},1\frac{7}{8},1.75,2.4$.

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 $2\frac{1}{4},1\frac{7}{8},1.75,2.4$.”

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, $2\frac{1}{4}$will be written as,

$2\frac{1}{4}=\frac{\left(2\times 4\right)+1}{4}$

$2\frac{1}{4}=\frac{9}{4}$

And, $1\frac{7}{8}$will be written as,

$1\frac{7}{8}=\frac{\left(1\times 8\right)+7}{8}$

$1\frac{7}{8}=\frac{15}{8}$

Step 4. Rewrite.

Now, convert $\frac{9}{4}$and $\frac{15}{8}$into decimal notation and then compare the set of rational numbers.

Decimal notation for $\frac{9}{4}$is 2.25.

Decimal notation for $\frac{15}{8}$is $1.875$.

Thus, the set of rational number $2\frac{1}{4},1\frac{7}{8},1.75,2.4$becomes $2.25,1.875,1.75,2.4$.

Step 5. Arrangement.

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

$1.75<1.875<2.25<2.4$

$1.75<1\frac{7}{8}<2\frac{1}{4}<2.4$

Hence, the correct order of rational numbers from least to greatest is $1.75<1\frac{7}{8}<2\frac{1}{4}<2.4$.