Question

Which number has the greatest value? (1 point)
Responses

123
1 and 2 thirds

2–√
square root of 2

π2
pi over 2

1.5

Answer 1

To determine which number has the greatest value, let's evaluate each option:

1. **123**: This is a whole number.
2. **1 and 2 thirds**: This is equivalent to \(1 + \frac{2}{3} = 1.666...\)
3. **\(2 - \sqrt{2}\)**: The square root of 2 is approximately 1.414, so \(2 - \sqrt{2} \approx 2 - 1.414 = 0.586\).
4. **\(\frac{\pi}{2}\)**: Pi (π) is approximately 3.14, so \(\frac{\pi}{2} \approx \frac{3.14}{2} \approx 1.57\).
5. **1.5**: This is a decimal number.

Now, let's approximate the values:

- \(123 = 123\)
- \(1 + \frac{2}{3} \approx 1.666...\)
- \(2 - \sqrt{2} \approx 0.586\)
- \(\frac{\pi}{2} \approx 1.57\)
- \(1.5 = 1.5\)

Now comparing these values:
- 123
- 1.666...
- 0.586
- 1.57
- 1.5

Clearly, the greatest value is **123**.