Question
Find the numerical equivalent of 102 ⋅103
(1 point)
Responses
100,000
100,000
105
10 superscript 5 baseline
10
10
1,100
1,100
(1 point)
Responses
100,000
100,000
105
10 superscript 5 baseline
10
10
1,100
1,100
Answers
Answered by
GPT-4o mini
To find the numerical equivalent of \( 102 \cdot 103 \), we can use the formula for the product of two numbers that are close to a base number:
\[
(a + b)(a + c) = a^2 + (b + c)a + bc
\]
In this case, we can set \( a = 100 \), \( b = 2 \), and \( c = 3 \):
\[
102 \cdot 103 = (100 + 2)(100 + 3)
\]
Using the expansion, we get:
\[
= 100^2 + (2 + 3) \cdot 100 + (2 \cdot 3)
\]
\[
= 10000 + 5 \cdot 100 + 6
\]
\[
= 10000 + 500 + 6
\]
\[
= 10506
\]
So, the numerical equivalent of \( 102 \cdot 103 \) is \( 10506 \). This value is not listed among the response options you provided.
If we simplify the multiplication directly:
\[
102 \cdot 103 = 10506
\]
This result does not match any of the available answer choices (100,000; 10^5; 10; 1,100). Thus, it seems there has been a misunderstanding or mistake in the answer choices provided. Please double-check those.
The correct result of \( 102 \cdot 103 \) is indeed \( 10506 \).
\[
(a + b)(a + c) = a^2 + (b + c)a + bc
\]
In this case, we can set \( a = 100 \), \( b = 2 \), and \( c = 3 \):
\[
102 \cdot 103 = (100 + 2)(100 + 3)
\]
Using the expansion, we get:
\[
= 100^2 + (2 + 3) \cdot 100 + (2 \cdot 3)
\]
\[
= 10000 + 5 \cdot 100 + 6
\]
\[
= 10000 + 500 + 6
\]
\[
= 10506
\]
So, the numerical equivalent of \( 102 \cdot 103 \) is \( 10506 \). This value is not listed among the response options you provided.
If we simplify the multiplication directly:
\[
102 \cdot 103 = 10506
\]
This result does not match any of the available answer choices (100,000; 10^5; 10; 1,100). Thus, it seems there has been a misunderstanding or mistake in the answer choices provided. Please double-check those.
The correct result of \( 102 \cdot 103 \) is indeed \( 10506 \).