Question
An expression is shown.
(7.6 × 103)(4.01 × 102) + (6.54 × 105)
Which expression is equivalent?
Responses
A (5.5 × 103)(7.4 × 103)(5.5 × 10 3 )(7.4 × 10 3 )
B (4.30 × 103)(7.03 × 103)(4.30 × 10 3 )(7.03 × 10 3 )
C (5.0 × 103)(7.4032 × 103)(5.0 × 10 3 )(7.4032 × 10 3 )
D (5.0 × 103)(7.4032 × 102)(5.0 × 10 3 )(7.4032 × 10 2 )
(7.6 × 103)(4.01 × 102) + (6.54 × 105)
Which expression is equivalent?
Responses
A (5.5 × 103)(7.4 × 103)(5.5 × 10 3 )(7.4 × 10 3 )
B (4.30 × 103)(7.03 × 103)(4.30 × 10 3 )(7.03 × 10 3 )
C (5.0 × 103)(7.4032 × 103)(5.0 × 10 3 )(7.4032 × 10 3 )
D (5.0 × 103)(7.4032 × 102)(5.0 × 10 3 )(7.4032 × 10 2 )
Answers
GPT-4o mini
To simplify the given expression \((7.6 \times 10^3)(4.01 \times 10^2) + (6.54 \times 10^5)\), we first need to calculate the multiplication part:
1. Multiply the first two terms:
\[
(7.6 \times 10^3)(4.01 \times 10^2) = 7.6 \times 4.01 \times 10^{3 + 2} = 30.556 \times 10^5
\]
We can express this in standard scientific notation:
\[
30.556 \times 10^5 = 3.0556 \times 10^6
\]
2. Now add the second term \((6.54 \times 10^5)\):
To do this effectively, we convert \((6.54 \times 10^5)\) to the same power as \(3.0556 \times 10^6\):
\[
6.54 \times 10^5 = 0.654 \times 10^6
\]
3. Now, add:
\[
3.0556 \times 10^6 + 0.654 \times 10^6 = (3.0556 + 0.654) \times 10^6 = 3.7096 \times 10^6
\]
Now we need to find an equivalent expression from the provided options:
Let's evaluate each one:
A: \( (5.5 \times 10^3)(7.4 \times 10^3) \) can be computed.
The product \( (5.5 \times 7.4) = 40.7 \), therefore:
\[
(5.5 \times 10^3)(7.4 \times 10^3) = 40.7 \times 10^6
\]
B: Similarly, find \( (4.30 \times 10^3)(7.03 \times 10^3) \):
The product \( (4.30 \times 7.03) \neq 3.7096 \), hence, skip.
C: Compute \( (5.0 \times 10^3)(7.4032 \times 10^3) \):
The product \( (5.0 \times 7.4032) = 37.016 \), \( \neq 3.7096 \times 10^6 \), hence, skip.
D: Now check \( (5.0 \times 10^3)(7.4032 \times 10^2) \):
The product \( (5.0 \times 7.4032 = 37.016) \times 10^5 \) can again reject.
After evaluating all options, none of the choices simplifies to \( \approx 3.7096 \times 10^6\).
**Correct answer**: None of the given options are equivalent to the calculated expression \(3.7096 \times 10^6\).
1. Multiply the first two terms:
\[
(7.6 \times 10^3)(4.01 \times 10^2) = 7.6 \times 4.01 \times 10^{3 + 2} = 30.556 \times 10^5
\]
We can express this in standard scientific notation:
\[
30.556 \times 10^5 = 3.0556 \times 10^6
\]
2. Now add the second term \((6.54 \times 10^5)\):
To do this effectively, we convert \((6.54 \times 10^5)\) to the same power as \(3.0556 \times 10^6\):
\[
6.54 \times 10^5 = 0.654 \times 10^6
\]
3. Now, add:
\[
3.0556 \times 10^6 + 0.654 \times 10^6 = (3.0556 + 0.654) \times 10^6 = 3.7096 \times 10^6
\]
Now we need to find an equivalent expression from the provided options:
Let's evaluate each one:
A: \( (5.5 \times 10^3)(7.4 \times 10^3) \) can be computed.
The product \( (5.5 \times 7.4) = 40.7 \), therefore:
\[
(5.5 \times 10^3)(7.4 \times 10^3) = 40.7 \times 10^6
\]
B: Similarly, find \( (4.30 \times 10^3)(7.03 \times 10^3) \):
The product \( (4.30 \times 7.03) \neq 3.7096 \), hence, skip.
C: Compute \( (5.0 \times 10^3)(7.4032 \times 10^3) \):
The product \( (5.0 \times 7.4032) = 37.016 \), \( \neq 3.7096 \times 10^6 \), hence, skip.
D: Now check \( (5.0 \times 10^3)(7.4032 \times 10^2) \):
The product \( (5.0 \times 7.4032 = 37.016) \times 10^5 \) can again reject.
After evaluating all options, none of the choices simplifies to \( \approx 3.7096 \times 10^6\).
**Correct answer**: None of the given options are equivalent to the calculated expression \(3.7096 \times 10^6\).