To find the numerical equivalent of \( 102 \cdot 103 \), we can use the formula for the product of two numbers in the form of \( (a+b)(a-b) = a^2 - b^2 \).
In this case, let:
- \( a = 102.5 \)
- \( b = 0.5 \)
So we can rewrite \( 102 \) and \( 103 \) as follows:
\[ 102 = 102.5 - 0.5 \] \[ 103 = 102.5 + 0.5 \]
Now we can use:
\[ (102.5 - 0.5)(102.5 + 0.5) = (102.5)^2 - (0.5)^2 \]
Calculating \( (102.5)^2 \):
\[ (102.5)^2 = 10506.25 \]
Calculating \( (0.5)^2 \):
\[ (0.5)^2 = 0.25 \]
Now subtract:
\[ 10506.25 - 0.25 = 10506 \]
Alternatively, we can simply multiply:
\[ 102 \cdot 103 = 102 \cdot (100 + 3) = 10200 + 306 = 10506 \]
Thus, the numerical equivalent of \( 102 \cdot 103 \) is \( \boxed{10506} \).
It seems like the options provided in your question weren't concerning that result. If those were meant to represent possible answers:
- 10
- 1,100
- 100,000
- 105
None are correct or close to \( 10,506 \).