Question
Evaluate. Express your answer in scientific notation.
9, point, 3, times, 10, to the power 5 , plus, 8, point, 2, times, 10, to the power 5
9, point, 3, times, 10, to the power 5 , plus, 8, point, 2, times, 10, to the power 5
Answers
Answered by
GPT-4o mini
To evaluate \( 9.3 \times 10^5 + 8.2 \times 10^5 \), we can combine the two terms since they both have the same exponent (10^5).
1. Add the coefficients:
\[
9.3 + 8.2 = 17.5
\]
2. Since both terms are multiplied by \( 10^5 \), we can write:
\[
17.5 \times 10^5
\]
3. Now, to express this in proper scientific notation, we need to convert 17.5 into a number between 1 and 10. We can do this by adjusting the number:
\[
17.5 = 1.75 \times 10^1
\]
4. Substituting this back, we rewrite it as:
\[
1.75 \times 10^1 \times 10^5 = 1.75 \times 10^{1+5} = 1.75 \times 10^6
\]
Thus, the final answer in scientific notation is:
\[
\boxed{1.75 \times 10^6}
\]
1. Add the coefficients:
\[
9.3 + 8.2 = 17.5
\]
2. Since both terms are multiplied by \( 10^5 \), we can write:
\[
17.5 \times 10^5
\]
3. Now, to express this in proper scientific notation, we need to convert 17.5 into a number between 1 and 10. We can do this by adjusting the number:
\[
17.5 = 1.75 \times 10^1
\]
4. Substituting this back, we rewrite it as:
\[
1.75 \times 10^1 \times 10^5 = 1.75 \times 10^{1+5} = 1.75 \times 10^6
\]
Thus, the final answer in scientific notation is:
\[
\boxed{1.75 \times 10^6}
\]