Question

order these numbers from least to greatest.
$9.\overline{5}$, $9\frac{4}{11}$, $-\sqrt{100}$, $9.46$

Explanation:

Step1: Convert all to decimals

• $9.\overline{5} = 9.555...$
• $9\frac{4}{11} = 9 + \frac{4}{11} \approx 9 + 0.3636 = 9.3636$
• $-\sqrt{100} = -10$
• $9.46$ remains $9.46$

Step2: Compare decimal values

$-10 < 9.3636 < 9.46 < 9.555...$

Answer:

$-\sqrt{100} < 9\frac{4}{11} < 9.46 < 9.\overline{5}$