Question

ordering rational numbers order the numbers from least to greatest. 15. $-3.1, -4, -\frac{10}{3}, -3\frac{3}{4}, -3.7$ 16. $3, -2\frac{2}{3}, 0, -\frac{3}{4}, -0.85$ 17. $\frac{3}{10}, -1\frac{1}{3}, 0.02, 1, -0.5$ 18. $-4.25, 1, -\frac{22}{5}, -4\frac{7}{8}, -3$

Explanation:

Step1: Convert all numbers to decimals

• \(-3.1\) is already a decimal.
• \(-4\) is an integer, decimal form: \(-4.0\)
• \(-\frac{10}{3} \approx -3.333\) (divide 10 by 3, take negative)
• \(-3\frac{3}{4} = -3.75\) (since \(\frac{3}{4}=0.75\))
• \(-3.7\) is already a decimal.

Step2: Order the decimals from least to greatest

Negative numbers with larger absolute values are smaller. So we compare the absolute values:
\(|-4.0| = 4.0\), \(|-3.75| = 3.75\), \(|-3.7| = 3.7\), \(|-3.333| = 3.333\), \(|-3.1| = 3.1\)

Order of absolute values (from largest to smallest): \(4.0 > 3.75 > 3.7 > 3.333 > 3.1\)

So the order of the negative numbers (from least to greatest) is: \(-4.0 < -3.75 < -3.7 < -3.333 < -3.1\)

Substituting back the original numbers: \(-4 < -3\frac{3}{4} < -3.7 < -\frac{10}{3} < -3.1\)

Answer:

\(-4, -3\frac{3}{4}, -3.7, -\frac{10}{3}, -3.1\)