College

Select all the correct answers.

What is [tex]$221,000,000,000,000,000,000$[/tex] expressed in scientific notation?

A. [tex]$2.21 \times 10^{20}$[/tex]
B. [tex]$221 \text{ E } 20$[/tex]
C. [tex]$221 \text{ E } 21$[/tex]
D. [tex]$2.21 \text{ E } -20$[/tex]
E. [tex]$2.21 \times 10^{-21}$[/tex]
F. [tex]$2.21 \times 10^{-20}$[/tex]
G. [tex]$221 \text{ E } -21$[/tex]

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]