To order the numbers from greatest to least, we first need to evaluate them:
- -0.0123456: This is a negative number, very close to zero.
- 3√27: This can be calculated as \(3 \times \sqrt{27} = 3 \times (3\sqrt{3}) = 9\sqrt{3}\). Since \(\sqrt{3} \approx 1.732\), \(9\sqrt{3} \approx 15.588\).
- 7/3: This is approximately \(2.333\).
- 0: This is zero.
- √15: This is approximately \(3.872\) (since \(\sqrt{15} \approx 3.872\)).
- -√45: This is negative, specifically \(\sqrt{45} = 3\sqrt{5}\), which is approximately \(6.708\), so \(-\sqrt{45} \approx -6.708\).
Now, let's summarize the approximate values:
- -0.0123456 (approximately -0.012)
- 3√27 (approximately 15.588)
- 7/3 (approximately 2.333)
- 0
- √15 (approximately 3.872)
- -√45 (approximately -6.708)
Now, ordering these from greatest to least:
- 3√27 (approximately 15.588)
- √15 (approximately 3.872)
- 7/3 (approximately 2.333)
- 0
- -0.0123456
- -√45 (approximately -6.708)
So, the final order from greatest to least is:
- 3√27
- √15
- 7/3
- 0
- -0.0123456
- -√45