Order -3, 5, 16 and -10 from least to greatest. Then order the same numbers from closest to zero to farthest from zero. Describe how your lists are similar. Would this be true if the numbers were -3, 5, -16, and -10.
-10 -3 5 16
vs
-3 5 -10 16
The second list would be unchanged if the new numbers were used.
Yes
To order the numbers -3, 5, 16, and -10 from least to greatest, you can simply compare the values.
Starting with the given numbers: -3, 5, 16, -10
Comparing -10 and -3, we see that -10 is smaller, so -10 comes first: -10
Next, comparing -10 and 5, we see that -10 is still smaller, so it remains first: -10, -3
Now, comparing -3 and 16, we see that -3 is smaller, so -3 comes before 16: -10, -3, 16
Finally, comparing 16 and 5, we see that 5 is smaller, so it comes last: -10, -3, 5, 16
Now, to order the same numbers from closest to zero to farthest from zero, we need to calculate the absolute value (distance from zero) for each number and then order accordingly.
The absolute value of -10 is 10.
The absolute value of -3 is 3.
The absolute value of 5 is 5.
The absolute value of 16 is 16.
Comparing the absolute values, we have: 3, 5, 10, 16
Therefore, the numbers from closest to zero to farthest from zero are: -3, 5, -10, 16
Comparing the two lists, we can see that the relative order remains the same, meaning that both lists start with the smallest value (-10), followed by the next smallest (-3), and so on. However, the second list considers the absolute values of the numbers, which allows us to determine their proximity to zero.
If the numbers were -3, 5, -16, and -10, the process would be the same for obtaining the ordered lists. Comparing absolute values, we get: 3, 5, 10, 16. Therefore, the lists would be the same: -3, 5, -10, 16.