Question

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

10
10

100,000
100,000

1,100
1,100

105

Answer 1

To find the numerical equivalent of \( 102 \cdot 103 \), we can use the formula for the product of two numbers that are close to 100:

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

In this case, \( a = 100 \), \( b = 2 \), and \( c = 3 \):

\[
102 \cdot 103 = (100 + 2)(100 + 3)
\]
\[
= 100^2 + (2 + 3) \cdot 100 + (2 \cdot 3)
\]
\[
= 10000 + 5 \cdot 100 + 6
\]
\[
= 10000 + 500 + 6
\]
\[
= 10506
\]

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

However, looking at your provided answers, it appears none of them match \( 10506 \). Could there be a misunderstanding about the options? Please verify or provide more context if needed!