Certainly! Let's break this down step by step.
### Part (a): Rounding to the nearest ten billionth of a meter
Firstly, the given diameter of a water molecule is [tex]\(0.00000000028\)[/tex] meters, which can be written as [tex]\(2.8 \times 10^{-10}\)[/tex] meters.
To round this number to the nearest ten billionth of a meter ([tex]\(10^{-10}\)[/tex] meters):
- Observe that the diameter is already very close to [tex]\(0.0000000003\)[/tex] meters (which equals [tex]\(3 \times 10^{-10}\)[/tex]).
- Therefore, when rounding [tex]\(0.00000000028\)[/tex] meters to the nearest ten billionth, we get [tex]\(0.0000000003\)[/tex] meters.
So, the rounded diameter is:
[tex]\[ 3 \times 10^{-10} \text{ meters} \][/tex]
### Part (b): Express the rounded diameter as a single digit times a unit fraction with a denominator written as a power of 10 in exponential form
The rounded diameter is [tex]\(0.0000000003\)[/tex] meters, which equals [tex]\(3 \times 10^{-10}\)[/tex] meters.
Now, let's express [tex]\(3 \times 10^{-10}\)[/tex] meters in the form of a single digit times a unit fraction:
- The number [tex]\(3 \times 10^{-10}\)[/tex] can be considered as a single digit (3) multiplied by the power of 10.
- In scientific notation, this is already in the desired form.
The exponential form is:
[tex]\[ 3 \times 10^{-10} \][/tex]
Thus:
1. Rounded to the nearest ten billionth of a meter: [tex]\(3 \times 10^{-10}\)[/tex] meters.
2. Expressed as a single digit times a unit fraction: [tex]\(3 \times 10^{-10}\)[/tex].
