Answer: To understand why you're not getting a perfect 0 when dividing 100 by 2 repeatedly, let's break down the problem step by step:
At the end of the first minute, the lizard travels half of the distance to the tree, which is 100 feet / 2 = 50 feet.
At the end of the second minute, the lizard again travels half of the remaining distance, which is half of 50 feet = 25 feet.
At the end of the third minute, the lizard once again travels half of the remaining distance, which is half of 25 feet = 12.5 feet.
Now, you might be wondering why you're not getting a perfect 0. The reason is that the lizard is approaching the tree by dividing the remaining distance in half each time, but it will never reach exactly 0 feet. This is a concept from mathematics called a geometric series or a "sum of infinite halves." The lizard can keep halving the remaining distance, but it will continue to approach the tree without reaching it.
If we calculate the sum of the infinite halves, it will approach the value of 100 feet, which is the original distance to the tree. However, the sum will never actually equal 100 feet.
So, in this case, the lizard will continue traveling towards the tree indefinitely but will never actually reach the tree by following this pattern.