Math

QuestionA beach erodes at 4 cm/year. Convert this to mm/day using the correct expression. Which one is right?

Studdy Solution

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 cm1 year ×10 mm1 cm×1 year 365 days \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 is4 cm1 year ×1 mm10 cm×1 year 365 days \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 10 mm1 cm\frac{10 \mathrm{~mm}}{1 \mathrm{~cm}}, not 1 mm10 cm\frac{1 \mathrm{~mm}}{10 \mathrm{~cm}}.

STEP 5

The third expression is4 cm1 year ×1 cm10 mm×365 days 1 year \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 10 mm1 cm\frac{10 \mathrm{~mm}}{1 \mathrm{~cm}} and 1 year 365 days \frac{1 \text { year }}{365 \text { days }}, not the other way around.

STEP 6

The fourth expression is4 cm1 year ×10 mm1 cm×365 days 1 year \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 1 year 365 days \frac{1 \text { year }}{365 \text { days }}, not 365 days 1 year \frac{365 \text { days }}{1 \text { year }}.

STEP 7

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 is4 cm1 year ×10 mm1 cm×1 year 365 days \frac{4 \mathrm{~cm}}{1 \text { year }} \times \frac{10 \mathrm{~mm}}{1 \mathrm{~cm}} \times \frac{1 \text { year }}{365 \text { days }}

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