Question

Find the numerical equivalent of 102 ⋅103(1 point)
Responses

100,000
100,000
1,100
1,100
10
10
105

Answer 1

To find the numerical equivalent of \( 102 \cdot 103 \), we can perform the multiplication directly.

Calculating \( 102 \cdot 103 \):

\[
102 \cdot 103 = 102 \cdot (100 + 3) = 102 \cdot 100 + 102 \cdot 3
\]

Calculating each part:

\[
102 \cdot 100 = 10200
\]
\[
102 \cdot 3 = 306
\]

Now, add these results together:

\[
10200 + 306 = 10506
\]

Thus, the numerical equivalent of \( 102 \cdot 103 \) is \( 10506 \).

However, this doesn't match any of the provided responses, so let's check the options again:

- 100,000
- 1,100
- 10
- 105

None of these options are correct based on our calculation. If we re-evaluate, we can also use the formula for the product of two numbers close to 100:

\[
(a + b)(a + c) = a^2 + (b + c)a + bc
\]

Here, \( a = 100 \), \( b = 2 \), and \( c = 3 \):

\[
100^2 + (2 + 3)100 + (2 \cdot 3)
\]
\[
= 10000 + 500 + 6
\]
\[
= 10506
\]

Again, it confirms that \( 102 \cdot 103 = 10506 \). Since the answers provided do not include 10506, there's an error in the choices or options.

Thus, the correct numerical equivalent is \( 10506 \), but it's not in the responses provided.