Question

Find the sum. Write your answer in scientific notation, with the decimal to the nearest thousandth.
(1.37 x 10^(12)( + (23.47 x 10^(14))

Answer 1

To find the sum of \( 1.37 \times 10^{12} + 23.47 \times 10^{14} \), we first need to express both numbers with the same exponent.

The exponent \( 10^{14} \) is larger, so we will convert \( 1.37 \times 10^{12} \) into the same order of magnitude:

\[
1.37 \times 10^{12} = 0.0137 \times 10^{14}
\]

Now, we can rewrite the sum:

\[
0.0137 \times 10^{14} + 23.47 \times 10^{14} = (0.0137 + 23.47) \times 10^{14}
\]

Calculating the sum inside the parentheses:

\[
0.0137 + 23.47 = 23.4837
\]

Now we can write it in scientific notation:

\[
23.4837 \times 10^{14}
\]

To convert \( 23.4837 \) into scientific notation, we shift the decimal one place to the left:

\[
23.4837 = 2.34837 \times 10^{1}
\]

Thus, combining this with \( 10^{14} \):

\[
23.4837 \times 10^{14} = 2.34837 \times 10^{1} \times 10^{14} = 2.34837 \times 10^{15}
\]

Finally, rounding \( 2.34837 \) to the nearest thousandth gives us \( 2.348 \).

Thus, the final answer in scientific notation is:

\[
\boxed{2.348 \times 10^{15}}
\]