Question

The order of the set of rational numbers $0.11, -\frac{1}{9}, -0.5, \frac{1}{10}$from least to greatest.

Short answer

The correct order of rational numbers from least to greatest is $-0.5, -\frac{1}{9}, \frac{1}{10},0.11$.

Step-by-step solution

Step 1.

The set of rational numbers $0.11,-\frac{1}{9},-0.5,\frac{1}{10}$.

Step 2. Formula Used.

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

Step 3. Calculation.

Consider the provided statement “The set of rational numbers $0.11,-\frac{1}{9},-0.5,\frac{1}{10}$.”

Convert $-\frac{1}{9}$and $\frac{1}{10}$into decimal notation and then compare the set of rational numbers.

Decimal notation for $-\frac{1}{9}$is $-0.\overline{1}$.

Decimal notation for $\frac{1}{10}$is 0.1.

Step 4. Rewrite.

Thus, the set of rational number $0.11,-\frac{1}{9},-0.5,\frac{1}{10}$ becomes $0.11,-0.\overline{1},-0.5,0.1$.

Step 5. Arrangement.

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

$-0.5<-0.\overline{1}<0.1<0.11$

$-0.5<-\frac{1}{9}<\frac{1}{10}<0.11$

Hence, the correct order of rational numbers from least to greatest is $-0.5<-\frac{1}{9}<\frac{1}{10}<0.11$.