Question

order these numbers from least to greatest.
$-dfrac{83}{7}$, $-sqrt{133}$, $11dfrac{5}{10}$, $-11.overline{6}$
note that for this question you can use your mouse to drag the numbers into their positions.
$-11.overline{6}$ $<$ $-sqrt{133}$ $<$ $11dfrac{5}{10}$ $<$ $-dfrac{83}{7}$

Explanation:

Step1: Convert to decimal values

$-\frac{83}{7} \approx -11.857$, $-\sqrt{133} \approx -11.532$, $11\frac{5}{10}=11.5$, $-11.\overline{6} \approx -11.667$

Step2: Compare negative decimals

Larger negative = smaller value: $-11.857 < -11.667 < -11.532$

Step3: Include positive number

Positive > all negatives: $-11.857 < -11.667 < -11.532 < 11.5$

Answer:

$-\frac{83}{7} < -11.\overline{6} < -\sqrt{133} < 11\frac{5}{10}$