Sure! Let's analyze the number 37,250 and find the value of the digit 7, which is located in the thousands place.
1. First Method: Direct Interpretation of Place Value
When looking at the number 37,250, we observe that the digit 7 is in the thousands place. The place value of the digit 7 in the thousands place can be calculated as:
[tex]\[ 7 \times 1000 = 7000 \][/tex]
Therefore, the value of the digit 7 is 7,000.
2. Second Method: Cumulative Value Up to the Thousands Place
Alternatively, we can calculate the value of the digit 7 by first considering the entire left part of the number (up to and including the digit 7).
The first two digits of the number 37,250 are 37. When we consider these two digits as a whole, we have:
[tex]\[ 37 \times 1000 = 37000 \][/tex]
This represents the total value contributed by the digits 3 and 7 in the ten-thousands and thousands places, respectively. However, to isolate the specific contribution of the digit 7 in the thousands place, we subtract the contribution of the digit 3 in the ten-thousands place:
[tex]\[ 37000 - 30000 = 7000 \][/tex]
So, the cumulative value including the digit 3 combined with the digit 7 also helps us confirm that the contribution of the digit 7 alone is 7,000.
In conclusion, the value of the digit 7 in the number 37,250 can be expressed in two ways as:
1. 7,000 (from the direct place value).
2. 37,000 (cumulative value up to the thousands place).
However, for clarity, it's important to note that 37,000 includes the contribution of both digits 3 and 7 in their respective places, and the actual specific contribution of the digit 7 alone remains 7,000.
