(4.54 × 104) × (2.5 × 10-2)

(2.5 × 103)
What is the value of the expression above?

Responses
A 45,40045,400
B 453.57453.57
C 43,78843,788
D 0.454

1 answer

To evaluate the expression \((4.54 \times 10^4) \times (2.5 \times 10^{-2}) \div (2.5 \times 10^3)\), we can break it down step by step.

  1. Multiply the first two terms:

    \[ (4.54 \times 10^4) \times (2.5 \times 10^{-2}) = (4.54 \times 2.5) \times (10^4 \times 10^{-2}) \]

    First, calculate \(4.54 \times 2.5\):

    \[ 4.54 \times 2.5 = 11.35 \]

    And add the exponents for the powers of 10:

    \[ 10^4 \times 10^{-2} = 10^{4 - 2} = 10^2 \]

    So, we have:

    \[ 11.35 \times 10^2 \]

  2. Now we can simplify the division part with the result obtained:

    \[ (11.35 \times 10^2) \div (2.5 \times 10^3) = \frac{11.35}{2.5} \times \frac{10^2}{10^3} \]

    Calculating \(\frac{11.35}{2.5}\):

    \[ \frac{11.35}{2.5} = 4.54 \]

    And for the powers of 10:

    \[ \frac{10^2}{10^3} = 10^{2 - 3} = 10^{-1} \]

    Now, we combine these:

    \[ 4.54 \times 10^{-1} \]

  3. Final calculation:

    \[ 4.54 \times 10^{-1} = 0.454 \]

Thus, the value of the expression is \(0.454\).

The correct answer is D: 0.454.