Explain the place value relationship when the same two digits are next to each other in a multi digit number
The Correct Answer and Explanation is:
When the same two digits are next to each other in a multi-digit number, their place value relationship depends on the position of each digit within the number. The place value of a digit is determined by both its value and its position in the number. In a multi-digit number, each digit has a place value based on the powers of 10.
For example, consider the number 3356. In this case, we have two “3”s next to each other in the thousands and hundreds places. The first “3” (on the left) is in the thousands place, so its value is 3 * 1000 = 3000. The second “3” is in the hundreds place, so its value is 3 * 100 = 300. Therefore, the total contribution from the two “3”s is 3000 + 300 = 3300.
Now, let’s think about the relationship between these two identical digits. When two digits are the same and placed in adjacent places, the total value of those two digits is simply the sum of the individual values of each place. The importance of place value becomes clearer here, as the digit in the higher place (leftmost) will contribute significantly more than the digit in the lower place (rightmost).
So, in a number like 1124, the “1”s are in the thousands and hundreds places, contributing 1000 and 100 respectively. The place value difference between them is ten times, meaning that the “1” in the thousands place is ten times more significant than the “1” in the hundreds place.
In summary, when two identical digits are next to each other in a multi-digit number, their place value relationship emphasizes the fact that each digit’s contribution depends on both its magnitude and its position relative to the other digits. The leftmost digit always has a higher value due to its position in the number system.
