Question

Annual Statistics Concerning Coastal Erosion

California coast lines are eroding at a rate of 30 centimeters per year/ Louisiana coast lines are eroding at a rate of 10 meters per year

a. Choose the appropriate unit and then use technology to convert the numbers to scientific notation.
California Coastal Erosion: Louisiana Coastal Erosion:

b. Compare the values. How many times greater is the coastal erosion in Louisiana?

Answer 1

A) 3×10¹ cm/year and 1×10³ cm/year

We have two data with different units: 10 m/year and 30 cm/year.

We need to transform one of the units in order to be able to compare the two numbers, therefore we decide to trasform everything in the smallest unit, which is centimeter per year.

There are 100 cm in 1 meter, therefore:

`10 m \cdot (100 cm)/(1 m) = 1000 cm`

Now, let's trasform the number into scientific notation. The scientific notation is composed by a number with only 1 digit to the left of the point multiplyed by a 10 to the power of how many spaces you moved the point from the original number:
30 = 3×10¹
1000 = 1×10³

Hence, the answer is 3×10¹ cm/year and 1×10³ cm/year

B) The coastal erosion in Louisiana is 100 times greater than in California.

When comparing two numbers written in scientific notation, you only compare the order of magnitude, which is given by the power of 10, by dividing them:
10³ ÷ 10¹ = 10² = 100

Hence, the answer is the coastal erosion in Louisiana is 100 times greater than in California