To convert the erosion rate from centimeters per year to millimeters per day, we need to properly account for the unit conversions:
1. Convert centimeters to millimeters:
- We know that 1 centimeter (cm) equals 10 millimeters (mm).
2. Express the erosion rate in millimeters per year:
- If the erosion rate is 4 cm/year, we should convert that to millimeters.
- [tex]\( 4 \text{ cm/year} \times 10 \text{ mm/cm} = 40 \text{ mm/year} \)[/tex]
3. Convert years to days:
- There are 365 days in a year.
4. Express the erosion rate in millimeters per day:
- Divide the annual erosion rate in millimeters by the number of days in a year.
- [tex]\( \frac{40 \text{ mm/year}}{365 \text{ days/year}} \approx 0.1095890410958904 \text{ mm/day} \)[/tex]
So, step-by-step:
- Begin with [tex]\( \frac{4 \text{ cm}}{1 \text{ year}} \)[/tex]
- Convert to millimeters: [tex]\( \frac{4 \text{ cm}}{1 \text{ year}} \times \frac{10 \text{ mm}}{1 \text{ cm}} = \frac{40 \text{ mm}}{1 \text{ year}} \)[/tex]
- Convert years to days: [tex]\( \frac{40 \text{ mm/year}}{365 \text{ days/year}} \approx 0.1095890410958904 \text{ mm/day} \)[/tex]
Therefore, the correct expression that results in the correct units and numerical value is:
[tex]\[ \frac{4 \text{ cm}}{1 \text{ year}} \times \frac{10 \text{ mm}}{1 \text{ cm}} \times \frac{1 \text{ year}}{365 \text{ days}} \][/tex]
Evaluating this expression gives us the correct units (mm/day) and the correct numerical value, approximately [tex]\( 0.1095890410958904 \text{ mm/day} \)[/tex].
