Question

Jeff placed the following numbers from least to greatest on a number line. On which number line do the numbers appear in the correct order: 2.9, √10, 7/3, 2√2?

A. 2.9, √10, 7/3, 2√2
B. √10, 2.9, 7/3, 2√2
C. 7/3, 2.9, √10, 2√2
D. 2√2, 2.9, 7/3, √10

Answer 1

The correct order of numbers from least to greatest is √10, 2.9, 7/3, and 2√2, which corresponds to Option B. This is determined by calculating or estimating the decimal values of the square roots and the fraction.

Step-by-step explanation:

To place the numbers 2.9, √10, 7/3, and 2√2 from least to greatest, we need to understand their approximate values or calculate them explicitly. The fraction 7/3 is equal to 2.333..., which we could round to 2.33 for comparison purposes. To estimate √10, we know that √9 = 3 and √16 = 4, so √10 must be between 3 and 4; a calculator would show it is approximately 3.16. Similarly, 2√2 can be estimated knowing that √2 is about 1.41, so 2√2 is approximately 2.82. Now we compare these approximate values:

• 7/3 ≈ 2.33
• 2.9 is already given as a decimal
• √10 ≈ 3.16
• 2√2 ≈ 2.82

Arranging these from least to greatest, we obtain: 2.9 (> 2√2 > √10 > 7/3. Comparing this order with the provided options, we find that the correct order is listed in Option B as √10, 2.9, 7/3, 2√2.