Scientific notation commonly results when we work with units of measure. Solve the following problem with a unit analysis and assume 365 days per year. Round the decimal part of your answer to two decimal places. How fast in feet per second is a silver birch tree growing if it is 20 feet tall after 10 years of growth?
A) $6.64 \times 10 ^ { - 6 }$ feet per second
B) $5.9 \times 10 ^ { - 9 }$ feet per second
C) $6.34 \times 10 ^ { - 7 }$ feet per second
D) $5.9 \times 10 ^ { - 8 }$ feet per second
E) $6.34 \times 10 ^ { - 8 }$ feet per second

Question

Quizplus · Accepted Answer

Let's start by using the formula:

velocity = distance / time

We want to find the velocity in feet per second, which means our distance needs to be in feet and our time needs to be in seconds. We know that the tree grew 20 feet in 10 years, so we can find the velocity by:

velocity = (20 feet) / (10 years x 365 days/year x 24 hours/day x 60 minutes/hour x 60 seconds/minute)

Note that we converted years to days, days to hours, hours to minutes, and minutes to seconds to get our time in seconds. Now we can simplify:

velocity = (20 feet) / (3.1536 x 10^8 seconds)

velocity = 6.33 x 10^-8 feet per second

Rounding to two decimal places gives us:

velocity = 6.34 x 10^-8 feet per second

Therefore, the answer is E.

Scientific Notation Commonly Results When We Work with Units of Measure