Let's convert the given diameter of a hydrogen atom, [tex]\(0.000000000106 \, \text{m}\)[/tex], into scientific notation.
### Step-by-Step Conversion to Scientific Notation
1. Identification of Key Digits:
- Identify the significant digits in the number. Here, significant digits are 1, 0, and 6.
2. Placement of the Decimal Point:
- Place the decimal point after the first non-zero digit. This gives [tex]\(1.06\)[/tex].
3. Counting the Exponential Shift:
- Determine how many places the decimal point has moved from its original position to its current position.
- Originally, the decimal point is at the leftmost position of the number [tex]\(0.000000000106\)[/tex].
- It has moved 10 places to get from [tex]\(0.000000000106\)[/tex] to [tex]\(1.06\)[/tex].
4. Assigning the Exponential Component:
- Because we moved the decimal point 10 places to the right, the exponent will be [tex]\(-10\)[/tex].
- Hence, the number in scientific notation is [tex]\(1.06 \times 10^{-10}\)[/tex].
#### Conclusion:
- We have expressed [tex]\(0.000000000106 \, \text{m}\)[/tex] as [tex]\(1.06 \times 10^{-10} \, \text{m}\)[/tex] in scientific notation.
### Verification:
Among the given options:
A. [tex]\(1.06 \times 10^{-9} \, \text{m}\)[/tex]
B. [tex]\(1.06 \times 10^{10} \, \text{m}\)[/tex]
C. [tex]\(10.6 \times 10^{-9} \, \text{m}\)[/tex]
D. [tex]\(1.06 \times 10^{-10} \, \text{m}\)[/tex]
The correct choice that matches our converted value is:
D. [tex]\(1.06 \times 10^{-10} \, \text{m}\)[/tex]
Therefore, the properly expressed scientific notation for the diameter of a hydrogen atom [tex]\(0.000000000106 \, \text{m}\)[/tex] is option D: [tex]\(1.06 \times 10^{-10} \, \text{m}\)[/tex].
