Math Snap

STEP 1

Assumptions1. The beach is eroding at a rate of4 centimeters per year.
. We need to convert this rate to millimeters per day.
3. The conversion factors are -1 cm =10 mm -1 year =365 days

STEP 2

To convert the rate of erosion from centimeters per year to millimeters per day, we need to multiply the given rate by the conversion factors. The correct expression should convert centimeters to millimeters and years to days.

STEP 3

The first expression is$$\frac{ \mathrm{~cm}}{1 \text { year }} \times \frac{10 \mathrm{~mm}}{1 \mathrm{~cm}} \times \frac{1 \text { year }}{365 \text { days }}$$This expression correctly converts centimeters to millimeters and years to days.

STEP 4

The second expression is$$\frac{4 \mathrm{~cm}}{1 \text { year }} \times \frac{1 \mathrm{~mm}}{10 \mathrm{~cm}} \times \frac{1 \text { year }}{365 \text { days }}$$This expression incorrectly converts centimeters to millimeters. The conversion factor should be $\frac{10 \mathrm{~mm}}{1 \mathrm{~cm}}$, not $\frac{1 \mathrm{~mm}}{10 \mathrm{~cm}}$.

STEP 5

The third expression is$$\frac{4 \mathrm{~cm}}{1 \text { year }} \times \frac{1 \mathrm{~cm}}{10 \mathrm{~mm}} \times \frac{365 \text { days }}{1 \text { year }}$$This expression incorrectly converts centimeters to millimeters and incorrectly converts years to days. The conversion factors should be $\frac{10 \mathrm{~mm}}{1 \mathrm{~cm}}$ and $\frac{1 \text { year }}{365 \text { days }}$, not the other way around.

STEP 6

The fourth expression is$$\frac{4 \mathrm{~cm}}{1 \text { year }} \times \frac{10 \mathrm{~mm}}{1 \mathrm{~cm}} \times \frac{365 \text { days }}{1 \text { year }}$$This expression incorrectly converts years to days. The conversion factor should be $\frac{1 \text { year }}{365 \text { days }}$, not $\frac{365 \text { days }}{1 \text { year }}$.

Based on the analysis of the four expressions, the first expression is the correct one. It correctly converts the rate of erosion from centimeters per year to millimeters per day.
So, the correct expression is$$\frac{4 \mathrm{~cm}}{1 \text { year }} \times \frac{10 \mathrm{~mm}}{1 \mathrm{~cm}} \times \frac{1 \text { year }}{365 \text { days }}$$