College

Which is equivalent to the following expression?

[tex](4 \times 10^8) + (3 \times 10^6) + (5 \times 10^5) + (1 \times 10^3) + (2 \times 10^2) + (8 \times 10^0)[/tex]

A) [tex]100,351,028[/tex]
B) [tex]403,501,208[/tex]
C) [tex]400,353,208[/tex]
D) [tex]403,053,208[/tex]

Answer :

To solve the expression [tex]\(\left(4 \times 10^8\right)+\left(3 \times 10^6\right)+\left(5 \times 10^5\right)+\left(1 \times 10^3\right)+\left(2 \times 10^2\right)+\left(8 \times 10^0\right)\)[/tex] and find its equivalent value, we need to evaluate each term and then sum them up. Here's how you do it step-by-step:

1. Evaluate each term:
- [tex]\(\left(4 \times 10^8\right)\)[/tex] evaluates to 400,000,000.
- [tex]\(\left(3 \times 10^6\right)\)[/tex] evaluates to 3,000,000.
- [tex]\(\left(5 \times 10^5\right)\)[/tex] evaluates to 500,000.
- [tex]\(\left(1 \times 10^3\right)\)[/tex] evaluates to 1,000.
- [tex]\(\left(2 \times 10^2\right)\)[/tex] evaluates to 200.
- [tex]\(\left(8 \times 10^0\right)\)[/tex] evaluates to 8.

2. Add the evaluated terms:
- Start by adding the first two: [tex]\(400,000,000 + 3,000,000 = 403,000,000\)[/tex].
- Add the next term: [tex]\(403,000,000 + 500,000 = 403,500,000\)[/tex].
- Continue adding: [tex]\(403,500,000 + 1,000 = 403,501,000\)[/tex].
- Add the next term: [tex]\(403,501,000 + 200 = 403,501,200\)[/tex].
- Finally, add the last term: [tex]\(403,501,200 + 8 = 403,501,208\)[/tex].

Therefore, the expression is equivalent to 403,501,208.

3. Select the answer choice:
- Looking at the options given, the correct choice is B) [tex]\(403,501,208\)[/tex].

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