To express the diameter of a carbon atom, [tex]\(0.000000000154\)[/tex] meters, in scientific notation, we follow these steps:
1. Identify the significant figures:
The given number is [tex]\(0.000000000154\)[/tex]. The significant figures here are 1, 5, and 4.
2. Place the decimal point to the right of the first significant figure:
We rewrite 0.000000000154 in the form of [tex]\(1.54 \times 10^n\)[/tex], where [tex]\(n\)[/tex] is an integer.
3. Count the number of decimal places the decimal point has moved to get from the original number to the new number:
In [tex]\(0.000000000154\)[/tex], the decimal point will need to move 10 places to the right to become [tex]\(1.54\)[/tex].
4. Determine the exponent:
Since the decimal point moved 10 places to the right, we represent this movement as a power of 10. As the movement was towards the left of the original decimal place, it will be a negative exponent.
Therefore, [tex]\(0.000000000154\)[/tex] can be written as [tex]\(1.54 \times 10^{-10}\)[/tex].
5. Select the correct answer from the choices provided:
- a. [tex]\(1.54 \times 10^{12} m\)[/tex]
- b. [tex]\(1.54 \times 10^{-12} m\)[/tex]
- c. [tex]\(1.54 \times 10^{10} m\)[/tex]
- d. [tex]\(1.54 \times 10^{-10} m\)[/tex]
The number [tex]\(1.54 \times 10^{-10} m\)[/tex] is the equivalent representation of [tex]\(0.000000000154 m\)[/tex]. Thus, the best answer is:
d. [tex]\(1.54 \times 10^{-10} m\)[/tex]
So, the correct choice is D.
