Question

An expression is shown.



(7.6 × 10^3)(4.01 × 10^2) + (6.54 × 10^5)


Which expression is equivalent?
Responses
A (5.5 × 10^3)(7.4 × 10^3)
B (4.30 × 10^3)(7.03 × 10^3)
C (5.0 × 10^3)(7.4032 × 10^3)
D (5.0 × 10^3)(7.4032 × 10^2)

Answer 1

To find an expression equivalent to \((7.6 \times 10^3)(4.01 \times 10^2) + (6.54 \times 10^5)\), we will first simplify the original expression.

1. Calculate the first term:
\[
(7.6 \times 10^3)(4.01 \times 10^2) = 7.6 \times 4.01 \times 10^{3+2} = 30.476 \times 10^5
\]

2. The second term is already \(6.54 \times 10^5\).

3. Now, we can combine the two terms:
\[
30.476 \times 10^5 + 6.54 \times 10^5 = (30.476 + 6.54) \times 10^5 = 37.016 \times 10^5
\]

Next, we should rewrite \(37.016 \times 10^5\) in scientific notation:
\[
37.016 \times 10^5 = 3.7016 \times 10^6
\]

Next, let's examine the provided options:

A. \((5.5 \times 10^3)(7.4 \times 10^3)\)
\[
= 5.5 \times 7.4 \times 10^{3+3} = 40.7 \times 10^6 \quad (\text{not equivalent})
\]

B. \((4.30 \times 10^3)(7.03 \times 10^3)\)
\[
= 4.30 \times 7.03 \times 10^{3+3} = 30.229 \times 10^6 \quad (\text{not equivalent})
\]

C. \((5.0 \times 10^3)(7.4032 \times 10^3)\)
\[
= 5.0 \times 7.4032 \times 10^{3+3} = 37.016 \times 10^6 \quad (\text{equivalent})
\]

D. \((5.0 \times 10^3)(7.4032 \times 10^2)\)
\[
= 5.0 \times 7.4032 \times 10^{3+2} = 37.016 \times 10^5 \quad (\text{not equivalent})
\]

Thus, the only equivalent expression is:

**C. (5.0 × 10^3)(7.4032 × 10^3)**.