# How do you order the rational numbers from least to greatest: 0.11, -1/9, -0.5, 1/10?

Oct 25, 2016

Numbers from least to greatest are $\left\{- 0.5 , - \frac{1}{9} , \frac{1}{10} , 0.11\right\}$

#### Explanation:

The easiest way to order rational numbers is to write them so that they are up to same places of decimal.

Here $- \frac{1}{9} = - 0.11111111111111 \ldots \ldots$, where number $1$ repeats endlessly, but other numbers do not last beyond hundredth place (i.e. second place after decimal point), hence we write numbers say upto five places only. Then

$0.11 = 0.11000$
$- \frac{1}{9} = - 0.11111$
$- 0.5 = - 0.50000$
$\frac{1}{10} = 0.10000$

It is apparent that least number is one with negative sign but highest absolute (or numerical) value and among these it is $- 0.50000$ or $- 0.5$, then comes $- 0.11111 = - \frac{1}{9}$ and then we positive numbers of which $0.10000 = \frac{1}{10}$ is least and greatest is $0.11000 = 0.11$.

Hence, numbers from least to greatest are $\left\{- 0.5 , - \frac{1}{9} , \frac{1}{10} , 0.11\right\}$

Oct 29, 2016

Same thing as Shwetank but different approach using fractions

$- 0.5 \text{; "-1/9"; "1/10"; } 0.11$

#### Explanation:

Note that the word 'least' is like saying 'less than'
There is a big difference between less than and smaller.

$- 0.5 \equiv - \frac{1}{2}$

$- \frac{1}{9} \to - \frac{1}{9}$

$0.11 \equiv \frac{11}{100}$

$\frac{1}{10} \equiv \frac{10}{100}$

Now think of the position on the number line

$- \frac{1}{9}$ is closer to 0 than is $- \frac{1}{2.} \text{ }$ So $- \frac{1}{2}$ is less than $- \frac{1}{9}$

$\left(\frac{1}{10} \equiv \textcolor{red}{\frac{10}{100}}\right)$ is less than $\left(0.11 \equiv \textcolor{red}{\frac{11}{100}}\right)$

So we have in order from left to right on the number line:

$- \frac{1}{2} \text{; "-1/9"; "10/100"; } \frac{11}{100}$

$- 0.5 \text{; "-1/9"; "1/10"; } 0.11$