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

Responses

10
10

1,100
1,100

100,000
100,000

105

1 answer

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 \( 10,506 \).