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Answer :
To express the number [tex]\(221,000,000,000,000,000,000\)[/tex] in scientific notation, we follow these steps:
1. Identify the Significant Figures:
- The number is [tex]\(221,000,000,000,000,000,000\)[/tex], which is essentially [tex]\(221\)[/tex] followed by 18 zeros.
2. Place the Decimal Point:
- For scientific notation, the number should be expressed with a decimal point after the first non-zero digit. So, [tex]\(221\)[/tex] becomes [tex]\(2.21\)[/tex].
3. Count the Exponents:
- Since we moved the decimal point 20 places to the left to get from [tex]\(221,000,000,000,000,000,000\)[/tex] to [tex]\(2.21\)[/tex], we multiply by [tex]\(10^{20}\)[/tex] to convert it back.
So, the number [tex]\(221,000,000,000,000,000,000\)[/tex] in scientific notation is correctly expressed as [tex]\(2.21 \times 10^{20}\)[/tex].
Finally, let's see which options match this scientific notation:
- [tex]\(2.21 \times 10^{21}\)[/tex] - Incorrect, exponent is too high.
- [tex]\(221 E 20\)[/tex] - Incorrect, doesn't correctly format decimal or exponent.
- [tex]\(221 E 21\)[/tex] - Incorrect, exponent is too high and format is not standard.
- [tex]\(2.21E-20\)[/tex] - Incorrect, negative exponent.
- [tex]\(2.21 \times 10^{-21}\)[/tex] - Incorrect, negative exponent.
- [tex]\(2.21 \times 10^{-20}\)[/tex] - Incorrect, negative exponent.
- [tex]\(2.21 \times 10^{20}\)[/tex] - Correct.
- [tex]\(221 E-21\)[/tex] - Incorrect, negative exponent.
Therefore, the correct answers are:
- [tex]\(2.21 \times 10^{20}\)[/tex]
1. Identify the Significant Figures:
- The number is [tex]\(221,000,000,000,000,000,000\)[/tex], which is essentially [tex]\(221\)[/tex] followed by 18 zeros.
2. Place the Decimal Point:
- For scientific notation, the number should be expressed with a decimal point after the first non-zero digit. So, [tex]\(221\)[/tex] becomes [tex]\(2.21\)[/tex].
3. Count the Exponents:
- Since we moved the decimal point 20 places to the left to get from [tex]\(221,000,000,000,000,000,000\)[/tex] to [tex]\(2.21\)[/tex], we multiply by [tex]\(10^{20}\)[/tex] to convert it back.
So, the number [tex]\(221,000,000,000,000,000,000\)[/tex] in scientific notation is correctly expressed as [tex]\(2.21 \times 10^{20}\)[/tex].
Finally, let's see which options match this scientific notation:
- [tex]\(2.21 \times 10^{21}\)[/tex] - Incorrect, exponent is too high.
- [tex]\(221 E 20\)[/tex] - Incorrect, doesn't correctly format decimal or exponent.
- [tex]\(221 E 21\)[/tex] - Incorrect, exponent is too high and format is not standard.
- [tex]\(2.21E-20\)[/tex] - Incorrect, negative exponent.
- [tex]\(2.21 \times 10^{-21}\)[/tex] - Incorrect, negative exponent.
- [tex]\(2.21 \times 10^{-20}\)[/tex] - Incorrect, negative exponent.
- [tex]\(2.21 \times 10^{20}\)[/tex] - Correct.
- [tex]\(221 E-21\)[/tex] - Incorrect, negative exponent.
Therefore, the correct answers are:
- [tex]\(2.21 \times 10^{20}\)[/tex]
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