Question

Which of the following would be a reasonable estimate for the height of a skyscraper?

1 × 10^-8 feet 1 × 10^-3 feet
1 × 10^3 feet
1 × 10^8 feet

Answer 1

1 × 10^3 feet

Step-by-step explanation:

1 × 10⁻⁸ feet = 0.00000001 feet

1 × 10⁻³ feet = 0.001 feet

1 × 10³ feet = 1000 feet

`1\ mile=5280\ feet\\\Rightarrow 1\ feet=(1)/(5280)\ miles`

So,

`1000\ feet=(1000)/(5280)= 0.189\ miles`

1 × 10⁸ = 100000000

`100000000\ feet=(100000000)/(5280)=18939.39\ miles`

The first two are less than 1 feet.

The last one is very high to put it into context the tallest building (Burj Khalifa) is 1,918 feet.

So, the third one is the most acceptable.

Answer 2

A reasonable estimate is 1 x 10^3 feet. By elimination, the first and second can't be since it will yield a negative answer and height can't be negative. Next, the fourth option will yield almost 1800 miles tall which is an impossible height. So the third is the reasonable estimate. Hope it helps.