a particular beach is eroding at a rate of 4 centimeters per year. a realtor converts this rate to…

a particular beach is eroding at a rate of 4 centimeters per year. a realtor converts this rate to millimeters per day. which expression, when evaluated, results in the correct units and numerical value?\n$\frac{4 \text{cm}}{1 \text{year}} \times \frac{10 \text{mm}}{1 \text{cm}} \times \frac{1 \text{year}}{365 \text{days}}$\n$\frac{4 \text{cm}}{1 \text{year}} \times \frac{1 \text{mm}}{10 \text{cm}} \times \frac{1 \text{year}}{365 \text{days}}$\n$\frac{4 \text{cm}}{1 \text{year}} \times \frac{1 \text{cm}}{10 \text{mm}} \times \frac{365 \text{days}}{1 \text{year}}$\n$\frac{4 \text{cm}}{1 \text{year}} \times \frac{10 \text{mm}}{1 \text{cm}} \times \frac{365 \text{days}}{1 \text{year}}$

a particular beach is eroding at a rate of 4 centimeters per year. a realtor converts this rate to millimeters per day. which expression, when evaluated, results in the correct units and numerical value?\n$\frac{4 \text{cm}}{1 \text{year}} \times \frac{10 \text{mm}}{1 \text{cm}} \times \frac{1 \text{year}}{365 \text{days}}$\n$\frac{4 \text{cm}}{1 \text{year}} \times \frac{1 \text{mm}}{10 \text{cm}} \times \frac{1 \text{year}}{365 \text{days}}$\n$\frac{4 \text{cm}}{1 \text{year}} \times \frac{1 \text{cm}}{10 \text{mm}} \times \frac{365 \text{days}}{1 \text{year}}$\n$\frac{4 \text{cm}}{1 \text{year}} \times \frac{10 \text{mm}}{1 \text{cm}} \times \frac{365 \text{days}}{1 \text{year}}$

Answer

Explanation:

Step1: Convert cm to mm

We know $1\ \text{cm}=10\ \text{mm}$, so use the conversion factor $\frac{10\ \text{mm}}{1\ \text{cm}}$ to cancel cm units: $\frac{4\ \text{cm}}{1\ \text{year}} \times \frac{10\ \text{mm}}{1\ \text{cm}}$

Step2: Convert years to days

We know $1\ \text{year}=365\ \text{days}$, so use the conversion factor $\frac{1\ \text{year}}{365\ \text{days}}$ to cancel year units: $\frac{4\ \text{cm}}{1\ \text{year}} \times \frac{10\ \text{mm}}{1\ \text{cm}} \times \frac{1\ \text{year}}{365\ \text{days}}$

Step3: Verify unit cancellation

  • cm cancels out, year cancels out, leaving $\frac{\text{mm}}{\text{day}}$, the desired unit.

Answer:

$\boldsymbol{\frac{4\ \text{cm}}{1\ \text{year}} \times \frac{10\ \text{mm}}{1\ \text{cm}} \times \frac{1\ \text{year}}{365\ \text{days}}}$ (the first option)