Answer :
To solve the problem of determining the sum of [tex]\(26.5 \times 10^4 + 9.4 \times 10^4\)[/tex] and express it in scientific notation, follow these steps:
1. Understand the Values:
- We need to add [tex]\(26.5 \times 10^4\)[/tex] and [tex]\(9.4 \times 10^4\)[/tex].
2. Add the Values:
- Since the powers of 10 are the same ([tex]\(10^4\)[/tex]), we can directly add the coefficients (the numbers in front).
- [tex]\(26.5 + 9.4 = 35.9\)[/tex].
3. Keep the Power of 10:
- After summing the coefficients, attach the common power of 10 to the result.
- Therefore, [tex]\(35.9 \times 10^4\)[/tex].
4. Convert to Scientific Notation:
- The coefficient [tex]\(35.9\)[/tex] is not between 1 and 10, so we need to adjust it to fit the standard form of scientific notation.
- Move the decimal point one place to the left for [tex]\(35.9\)[/tex], making it [tex]\(3.59\)[/tex].
- Since we reduced the coefficient by a factor of 10, increase the exponent by 1 to adjust the number: [tex]\(3.59 \times 10^{4+1} = 3.59 \times 10^5\)[/tex].
5. Find the Correct Answer from the Options:
- From the given options:
- a) [tex]\(35.9 \times 10^9\)[/tex]
- b) [tex]\(3.59 \times 10^5\)[/tex]
- c) [tex]\(17.1 \times 10^4\)[/tex]
- d) [tex]\(17.1 \times 10^8\)[/tex]
- The correct answer is option b) [tex]\(3.59 \times 10^5\)[/tex].
By following these steps, the final result of the sum expressed in scientific notation is [tex]\(3.59 \times 10^5\)[/tex].
1. Understand the Values:
- We need to add [tex]\(26.5 \times 10^4\)[/tex] and [tex]\(9.4 \times 10^4\)[/tex].
2. Add the Values:
- Since the powers of 10 are the same ([tex]\(10^4\)[/tex]), we can directly add the coefficients (the numbers in front).
- [tex]\(26.5 + 9.4 = 35.9\)[/tex].
3. Keep the Power of 10:
- After summing the coefficients, attach the common power of 10 to the result.
- Therefore, [tex]\(35.9 \times 10^4\)[/tex].
4. Convert to Scientific Notation:
- The coefficient [tex]\(35.9\)[/tex] is not between 1 and 10, so we need to adjust it to fit the standard form of scientific notation.
- Move the decimal point one place to the left for [tex]\(35.9\)[/tex], making it [tex]\(3.59\)[/tex].
- Since we reduced the coefficient by a factor of 10, increase the exponent by 1 to adjust the number: [tex]\(3.59 \times 10^{4+1} = 3.59 \times 10^5\)[/tex].
5. Find the Correct Answer from the Options:
- From the given options:
- a) [tex]\(35.9 \times 10^9\)[/tex]
- b) [tex]\(3.59 \times 10^5\)[/tex]
- c) [tex]\(17.1 \times 10^4\)[/tex]
- d) [tex]\(17.1 \times 10^8\)[/tex]
- The correct answer is option b) [tex]\(3.59 \times 10^5\)[/tex].
By following these steps, the final result of the sum expressed in scientific notation is [tex]\(3.59 \times 10^5\)[/tex].