Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form. It is written as the product of a coefficient [tex]\(a\)[/tex] and a power of 10 (i.e., [tex]\(a \times 10^n\)[/tex]), where [tex]\(1 \leq a < 10\)[/tex] and [tex]\(n\)[/tex] is an integer. Let's evaluate each of the given expressions to determine if they fit this form.
1. [tex]\(6 \times 10^{11}\)[/tex]
- The coefficient here is 6, which lies between 1 and 10.
- The exponent is an integer (11).
- Therefore, [tex]\(6 \times 10^{11}\)[/tex] is written in scientific notation.
2. [tex]\(12 \times 10^{-8}\)[/tex]
- The coefficient here is 12, which does not lie between 1 and 10.
- Even though the exponent is an integer (-8), the coefficient disqualifies it from being in scientific notation.
- Therefore, [tex]\(12 \times 10^{-8}\)[/tex] is not written in scientific notation.
3. [tex]\(0.2 \times 10^5\)[/tex]
- The coefficient here is 0.2, which does not lie between 1 and 10.
- Even though the exponent is an integer (5), the coefficient disqualifies it from being in scientific notation.
- Therefore, [tex]\(0.2 \times 10^5\)[/tex] is not written in scientific notation.
4. [tex]\(8 \times 7^2\)[/tex]
- First, evaluate the expression [tex]\(7^2 = 49\)[/tex].
- Substitute back: [tex]\(8 \times 49 = 392\)[/tex].
- The resulting number 392 is neither written as a product of a number between 1 and 10 and a power of 10, nor is it in scientific notation directly.
- Therefore, [tex]\(8 \times 7^2\)[/tex] is not written in scientific notation.
Thus, the only number that is written in proper scientific notation is:
[tex]\[ 6 \times 10^{11} \][/tex]
