Suppose you are comparing two numbers that are greater than 1,000. 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.
4
If the first 3 digits are all the same, only the 4th digit will be the deciding one.
To find the smaller number when comparing two numbers greater than 1,000, you need to compare the digits from left to right until you find a pair that is different. The first pair of digits that differ will determine the relative sizes of the numbers.
Let's break it down step by step:
Step 1: Start from the leftmost digit of both numbers.
Step 2: Compare the digits at the same position in both numbers.
Step 3: If the digits are equal, move to the next position (to the right) and repeat step 2.
Step 4: If the digits differ, you have found the answer. The number with the smaller digit at that position is the smaller number overall.
For example, let's say we want to compare two numbers: 1,235 and 1,268.
Step 1: Start from the leftmost digit: 1,235 and 1,268.
Step 2: Compare the first digit: 1 vs. 1. They are equal.
Step 3: Move to the next digit: 2 vs. 2. They are equal.
Step 3: Move to the next digit: 3 vs. 6. They differ.
Step 4: Since 3 is smaller than 6, we can conclude that 1,235 is the smaller number.
So, in this case, we had to compare three pairs of digits (1 vs. 1, 2 vs. 2, 3 vs. 6) before finding the answer.
In general, the number of pairs you might have to compare before finding the answer depends on how many digits the numbers have in common before finding a difference. In this case, the answer is three pairs of digits.