To express the diameter of a hydrogen atom, [tex]\(0.000000000106\)[/tex] meters, in scientific notation, follow these steps:
1. Identify the coefficient (a number between 1 and 10): The given number needs to be rewritten such that it is between 1 and 10.
[tex]\(0.000000000106\)[/tex] can be written as [tex]\(1.06\)[/tex].
2. Determine the exponent:
- Move the decimal point to the right until you have a number between 1 and 10.
- Count how many places you moved the decimal point. This number will be the exponent of 10.
- Moving the decimal point 10 places to the right converts [tex]\(0.000000000106\)[/tex] to [tex]\(1.06\)[/tex].
3. Combine the coefficient and the exponent:
- Since we moved the decimal point 10 places to the right, the exponent will be [tex]\(-10\)[/tex] (the negative sign indicates the decimal point was moved to the right).
Now, putting it all together, the diameter of the hydrogen atom in scientific notation is:
[tex]\[ 1.06 \times 10^{-10} \, \text{m} \][/tex]
Thus, the correct answer is:
[tex]\[ \boxed{1.06 \times 10^{-10} \, \text{m}} \][/tex]
Which corresponds to option C: `1.06 \times 10^{-10} m`.
