Question
What is the sum of 6.3×10 power of three and 2.41×10 power of four use scientific notation to express your answer
Answers
GPT-4o mini
To find the sum of \(6.3 \times 10^3\) and \(2.41 \times 10^4\), we first need to express both numbers with the same exponent.
The term \(2.41 \times 10^4\) can be rewritten in terms of \(10^3\):
\[
2.41 \times 10^4 = 2.41 \times 10^4 \times \frac{10^{-1}}{10^{-1}} = 2.41 \times 10^3 \times 10 = 24.1 \times 10^3
\]
Now we can add \(6.3 \times 10^3\) to \(24.1 \times 10^3\):
\[
6.3 \times 10^3 + 24.1 \times 10^3 = (6.3 + 24.1) \times 10^3 = 30.4 \times 10^3
\]
Next, we need to express \(30.4 \times 10^3\) in proper scientific notation. Scientific notation requires that the coefficient be between 1 and 10. Thus, we convert it as follows:
\[
30.4 \times 10^3 = 3.04 \times 10^4
\]
So, the final result is:
\[
\boxed{3.04 \times 10^4}
\]
The term \(2.41 \times 10^4\) can be rewritten in terms of \(10^3\):
\[
2.41 \times 10^4 = 2.41 \times 10^4 \times \frac{10^{-1}}{10^{-1}} = 2.41 \times 10^3 \times 10 = 24.1 \times 10^3
\]
Now we can add \(6.3 \times 10^3\) to \(24.1 \times 10^3\):
\[
6.3 \times 10^3 + 24.1 \times 10^3 = (6.3 + 24.1) \times 10^3 = 30.4 \times 10^3
\]
Next, we need to express \(30.4 \times 10^3\) in proper scientific notation. Scientific notation requires that the coefficient be between 1 and 10. Thus, we convert it as follows:
\[
30.4 \times 10^3 = 3.04 \times 10^4
\]
So, the final result is:
\[
\boxed{3.04 \times 10^4}
\]