Question

order these numbers from least to greatest.
\frac{172}{10}, -sqrt{300}, -17.overline{3}, -17\frac{9}{26}
note that for this question you can use your mouse to drag the numbers into their positions.

Explanation:

Step1: Simplify the numbers

$\frac{172}{10}=17.2$, $-\sqrt{300}\approx - 17.32$, $-17.\overline{3}=-17.333\cdots$, $-17\frac{9}{26}=-\frac{17\times26 + 9}{26}=-\frac{441}{26}\approx - 16.96$

Step2: Compare the negative numbers

Among negative numbers, the larger the absolute - value, the smaller the number. $\vert-17.333\cdots\vert>\vert - 17.32\vert>\vert-16.96\vert$. So $-17.\overline{3}<- \sqrt{300}<-17\frac{9}{26}$

Step3: Compare with the positive number

Since $\frac{172}{10}=17.2$ is positive and the others are negative, $\frac{172}{10}$ is the largest.

Answer:

$-17.\overline{3}<-\sqrt{300}<-17\frac{9}{26}<\frac{172}{10}$