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Answer :
Sure! Let's go through each part of the question step-by-step:
### Convert to Standard Form:
1. [tex]\(6.5 \times 10^{-7}\)[/tex]
- To convert this to standard form, we move the decimal point 7 places to the left.
- The result is [tex]\(0.00000065\)[/tex].
2. [tex]\(1.5806 \times 10^4\)[/tex]
- To convert this to standard form, we move the decimal point 4 places to the right.
- The result is [tex]\(15806.0\)[/tex].
### Convert to Scientific Notation:
3. [tex]\(0.00675\)[/tex]
- In scientific notation, we need to express this number such that the decimal point is placed after the first non-zero digit.
- The result is [tex]\(6.7500 \times 10^{-3}\)[/tex].
4. [tex]\(2,780,000\)[/tex]
- In scientific notation, we need to express this number such that the decimal point is placed after the first non-zero digit.
- The result is [tex]\(2.8 \times 10^6\)[/tex].
### Determine if the number is correctly written in scientific notation. If not, correct it:
5. [tex]\(98.1 \times 10^2\)[/tex]
- For a number to be in proper scientific notation, the coefficient (number before the [tex]\( \times 10 \)[/tex]) should be between 1 and 10.
- Here, [tex]\(98.1\)[/tex] is not between 1 and 10. Therefore, it needs to be corrected.
- We can write [tex]\(98.1 \times 10^2\)[/tex] as [tex]\(9.81 \times 10^3\)[/tex].
6. [tex]\(0.7 \times 10^{-4}\)[/tex]
- Similarly, the coefficient should be between 1 and 10.
- Here, [tex]\(0.7\)[/tex] is not between 1 and 10.
- We can write [tex]\(0.7 \times 10^{-4}\)[/tex] as [tex]\(7.0 \times 10^{-5}\)[/tex].
So, summarizing the answers:
1. [tex]\(6.5 \times 10^{-7} = 0.00000065\)[/tex]
2. [tex]\(1.5806 \times 10^4 = 15806.0\)[/tex]
3. [tex]\(0.00675 = 6.7500 \times 10^{-3}\)[/tex]
4. [tex]\(2,780,000 = 2.8 \times 10^6\)[/tex]
5. [tex]\(98.1 \times 10^2\)[/tex] should be written as [tex]\(9.81 \times 10^3\)[/tex]
6. [tex]\(0.7 \times 10^{-4}\)[/tex] should be written as [tex]\(7.0 \times 10^{-5}\)[/tex]
### Convert to Standard Form:
1. [tex]\(6.5 \times 10^{-7}\)[/tex]
- To convert this to standard form, we move the decimal point 7 places to the left.
- The result is [tex]\(0.00000065\)[/tex].
2. [tex]\(1.5806 \times 10^4\)[/tex]
- To convert this to standard form, we move the decimal point 4 places to the right.
- The result is [tex]\(15806.0\)[/tex].
### Convert to Scientific Notation:
3. [tex]\(0.00675\)[/tex]
- In scientific notation, we need to express this number such that the decimal point is placed after the first non-zero digit.
- The result is [tex]\(6.7500 \times 10^{-3}\)[/tex].
4. [tex]\(2,780,000\)[/tex]
- In scientific notation, we need to express this number such that the decimal point is placed after the first non-zero digit.
- The result is [tex]\(2.8 \times 10^6\)[/tex].
### Determine if the number is correctly written in scientific notation. If not, correct it:
5. [tex]\(98.1 \times 10^2\)[/tex]
- For a number to be in proper scientific notation, the coefficient (number before the [tex]\( \times 10 \)[/tex]) should be between 1 and 10.
- Here, [tex]\(98.1\)[/tex] is not between 1 and 10. Therefore, it needs to be corrected.
- We can write [tex]\(98.1 \times 10^2\)[/tex] as [tex]\(9.81 \times 10^3\)[/tex].
6. [tex]\(0.7 \times 10^{-4}\)[/tex]
- Similarly, the coefficient should be between 1 and 10.
- Here, [tex]\(0.7\)[/tex] is not between 1 and 10.
- We can write [tex]\(0.7 \times 10^{-4}\)[/tex] as [tex]\(7.0 \times 10^{-5}\)[/tex].
So, summarizing the answers:
1. [tex]\(6.5 \times 10^{-7} = 0.00000065\)[/tex]
2. [tex]\(1.5806 \times 10^4 = 15806.0\)[/tex]
3. [tex]\(0.00675 = 6.7500 \times 10^{-3}\)[/tex]
4. [tex]\(2,780,000 = 2.8 \times 10^6\)[/tex]
5. [tex]\(98.1 \times 10^2\)[/tex] should be written as [tex]\(9.81 \times 10^3\)[/tex]
6. [tex]\(0.7 \times 10^{-4}\)[/tex] should be written as [tex]\(7.0 \times 10^{-5}\)[/tex]
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