Answer :
Sure! Let's evaluate the expression [tex]\($5.78 \times 10^5 + 1.69 \times 10^5\)[/tex] and express the answer in scientific notation.
### Step-by-Step Solution:
1. Understand the Problem:
We need to add two numbers given in scientific notation: [tex]\(5.78 \times 10^5\)[/tex] and [tex]\(1.69 \times 10^5\)[/tex].
2. Align the Exponents:
Both numbers already have the same exponent (10^5), so we can directly add their coefficients.
3. Add the Coefficients:
- The coefficients are 5.78 and 1.69.
- Add these coefficients together:
[tex]\[
5.78 + 1.69 = 7.47
\][/tex]
4. Combine with the Exponent:
- Since the exponents are the same, the sum in scientific notation combines this coefficient with the exponent of 10^5:
[tex]\[
7.47 \times 10^5
\][/tex]
Therefore, the result of [tex]\(5.78 \times 10^5 + 1.69 \times 10^5\)[/tex] expressed in scientific notation is:
[tex]\[
\boxed{7.47 \times 10^5}
\][/tex]
### Step-by-Step Solution:
1. Understand the Problem:
We need to add two numbers given in scientific notation: [tex]\(5.78 \times 10^5\)[/tex] and [tex]\(1.69 \times 10^5\)[/tex].
2. Align the Exponents:
Both numbers already have the same exponent (10^5), so we can directly add their coefficients.
3. Add the Coefficients:
- The coefficients are 5.78 and 1.69.
- Add these coefficients together:
[tex]\[
5.78 + 1.69 = 7.47
\][/tex]
4. Combine with the Exponent:
- Since the exponents are the same, the sum in scientific notation combines this coefficient with the exponent of 10^5:
[tex]\[
7.47 \times 10^5
\][/tex]
Therefore, the result of [tex]\(5.78 \times 10^5 + 1.69 \times 10^5\)[/tex] expressed in scientific notation is:
[tex]\[
\boxed{7.47 \times 10^5}
\][/tex]
