Question

1. How many different numbers are in the list: 1, -3, 3, 2, 0.5?

2. Make a new list containing the squares of all these numbers. What are the squares of the numbers in the list?
3. How many different numbers are in the new list created in question 2?
4. Explain why the two lists do not have the same number of different numbers. What is the reason for the difference in the number of unique numbers in the original list and the list of their squares?

Answer 1

The original list contains 5 different numbers. The new list created by squaring the numbers contains 4 different numbers. The lower number of unique numbers in the list of squares is due to the fact that squaring a negative number results in a positive number.

Step-by-step explanation:

The list contains 5 different numbers: 1, -3, 3, 2, and 0.5.

When we square these numbers, we get the following new list: 1, 9, 9, 4, and 0.25.

The new list created in question 2 contains 4 different numbers: 1, 9, 4, and 0.25.

The reason the two lists do not have the same number of different numbers is because squaring a negative number results in a positive number. So, the negative number -3 becomes 9 when squared, which is already in the new list. Therefore, the number of unique numbers in the list of squares is lower than the original list.