Question

Solve this problem , Make sure that it is in scientific notation format prior to solving. 32.8 + (8.03 x 10^-8) A. 32.8000000803 x 10^2 B. 3.2000000803 x 10^1 C. 8.03 x 10 ^ 2 D. 80.3 x 10^3

Answer 1

To solve the problem \( 32.8 + (8.03 \times 10^{-8}) \), we'll need to express both terms in scientific notation in a compatible manner before we can add them.

Firstly, we convert \( 32.8 \) into scientific notation:

1. Move the decimal point to the right two places:
\[
32.8 = 3.28 \times 10^1
\]

Next, we handle \( 8.03 \times 10^{-8} \), which is already in scientific notation.

Now, we must express \( 3.28 \times 10^1 \) in terms of the same power of ten as \( 8.03 \times 10^{-8} \). To do that, we can rewrite \( 3.28 \times 10^1 \) to match the exponent \( -8 \):

\[
3.28 \times 10^1 = 3.28 \times 10^{1 - 9} = 3.28 \times 10^{-8} \times 10^9 = 32.8 \times 10^{-8}
\]

Now we add the two terms:

\[
32.8 \times 10^{-8} + 8.03 \times 10^{-8} = (32.8 + 8.03) \times 10^{-8} = 40.83 \times 10^{-8}
\]

Now we convert \( 40.83 \) into proper scientific notation:

\[
40.83 = 4.083 \times 10^1
\]

So,

\[
40.83 \times 10^{-8} = 4.083 \times 10^{1 - 8} = 4.083 \times 10^{-7}
\]

Thus, the final result in scientific notation is \( 4.083 \times 10^{-7} \).

Now let's analyze the provided options:
A. \( 32.8000000803 \times 10^2 \)
B. \( 3.2000000803 \times 10^1 \)
C. \( 8.03 \times 10^2 \)
D. \( 80.3 \times 10^3 \)

None of these options correctly matches our answer \( 4.083 \times 10^{-7} \).

If you need any further assistance or clarifications, let me know!