Final answer:
To order the numbers -10.1, -10.01, -10.009, and -10 from greatest to least, consider how close they are to zero. The sequence is -10 (closest to zero), followed by -10.009, then -10.01, and finally -10.1 (farthest from zero).
Step-by-step explanation:
When you are asked to order numbers from greatest to least, like the set -10.1, -10.01, -10.009, and -10, the best approach is to look at the decimal values. Here, since all the numbers are negative, the number closest to zero is actually the greatest. Therefore, -10 is the greatest because it is closest to zero. The farther a negative number is from zero, the smaller it is, so the next greatest number would be -10.009 followed by -10.01, and finally -10.1 as the smallest.
To give you a clearer picture, let's consider another set of negative numbers as an example:
Ordered from greatest to least, we would have -0.99, -1.01, -1.02, and -1.03, since -0.99 is the closest to zero. Applying the same logic to the original question, the sequence when ordered from greatest to least would be -10, -10.009, -10.01, and then -10.1.