Suppose you are comparing two numbers that are greater than 100. You want to find the smaller of the numbers. How many pairs of digits might you have to compare before you have your answer? Explain
Actually, there is no way to tell.
If both numbers have n digits (n>=3) then you might have to compare n pairs of digits, if the first (n-1) digits of each are the same.
I think the implication here is that the numbers are between 100 and 999, so if the first two digits of each are the same, all 3 digits will have to be compared.
This just shows that problems must be carefully stated, even for 3rd-graders!
1500 and 200
To find the smaller of two numbers that are greater than 100, you need to compare their digits from left to right until you find a pair of digits that are different. Let's walk through the steps:
1. Start by comparing the leftmost digits of the two numbers. If they are different, you can determine which number is smaller by comparing their values. The number with the smaller leftmost digit is the smaller number. For example, if the first number is 246 and the second number is 218, then you can conclude that 218 is smaller because 2 is smaller than 2.
2. If the leftmost digits are the same, move to the next digit from left to right and compare them. Repeat this process until you find a pair of digits that are different. The number with the smaller digit in that position is the smaller number.
3. Once you have found a pair of digits that are different, you have found the smaller number. You don't need to continue comparing any further pairs of digits beyond that point.
Now, to answer the question, let's consider the worst-case scenario. Suppose both numbers have the same leftmost digit and all the subsequent digits are the same until the very last digit. In this case, you would have to compare every single digit in the numbers, which is equal to the number of digits in the numbers.
Therefore, the number of pairs of digits you might have to compare before finding the smaller number is equal to the number of digits in the numbers.