Order the following from least to greatest: 5/3, √2.7, 4, -7, -2, √7, -3, 6.2%, √36, -4, 127%, 9/7, √2.

Steps to Solve

1. Identify Each Expression We have the following mathematical expressions:

• $ \sqrt{7.4} $
• $ -7, -2, -\sqrt{7} $
• $ -6.2%, -\sqrt{36}, -4 $
• $ 12%, \frac{9}{7}, \sqrt{2} $

2. Calculate the Values We simplify each expression to find their numerical values:

• For $ \sqrt{7.4} $:

  • Approximate the square root: $ \sqrt{7.4} \approx 2.73 $

• For $ -7, -2, -\sqrt{7} $:

  • $ -7 $ is already negative.
  • $ -2 $ is also negative.
  • Approximate $ -\sqrt{7} \approx -2.65 $

• For $ -6.2% $ and others: Converting percentages to decimals:

  • $ -6.2% = -0.062 $
  • $ -\sqrt{36} = -6 $
  • $ -4 = -4 $

• For $ 12%, \frac{9}{7}, \sqrt{2} $:

  • $ 12% = 0.12 $
  • $ \frac{9}{7} \approx 1.29 $
  • Approximate $ \sqrt{2} \approx 1.41 $

3. Arrange Values from Least to Greatest Now we list all the simplified values:

• From the first group: $ 2.73 $
• From the second group: $ -7, -2, -2.65 $
• From the third group: $ -0.062, -6, -4 $
• From the last group: $ 0.12, 1.29, 1.41 $

Now we combine them all: $$ -7, -6, -4, -2.65, -2, -0.062, 0.12, 1.29, 1.41, 2.73 $$

4. Find the Proper Order Ordering these gives:

• $ -7, -6, -4, -2.65, -2, -0.062, 0.12, 1.29, 1.41, 2.73 $