Question

John Muir was an American naturalist born in Scotland on April 21, 1838. As one of the first advocates of the United States' wilderness preservation, Muir spent his career writing letters, essays and books about many of his experiences in the Sierra Nevada mountains, located in northern California. Muir's influence on the history of American wilderness continues to live on past his death (in the early twentieth century) as people of all ages visit and hike through the 221 miles of the John Muir Trail, named in Muir's honor. The trail begins in Yosemite National Park and concludes at Mount Whitney, which contains the highest peak of the continental United States.

The following table compares Mount Whitney"s height, in meters, to other monumental peaks of the world.

Mountain Location Height (in meters)
of Highest Peak
Mount Whitney California, United States 4,418.38 meters
Mount Fuji Fuji-Hakone-Izu National Park, Japan 3,775.86 meters
Mount Everest Great Himalayas of southern Asia 8,849.87 meters
Mount Kilimanjaro Tanzania, Africa 5,894.83 meters
Mount Olympus Mytikas, Greece 2,919.07 meters
Use the data in the table to complete Parts A, B, and C. In your final answers, include your work for all estimates and calculations.

Part A:

Use scientific notation to estimate the following:
How many times greater is Mount Everest's highest peak than Mount Olympus's?

Part B:

Use scientific notation to calculate the following:
How many times greater is Mount Everest's highest peak than Mount Olympus's?

Part C:

Given the calculation in Part B comparing the highest peaks of Mount Everest and Mount Olympus, can you conclude that the estimate in Part A is reasonable? Answer in complete sentences. ( Write it out!!!)

Answer 1

A) ≈3

B) ≈3

C) See below.

Explanation:

Mount Everest is 8,849.87 meters tall.

Mount Olympus is 2,919.07 meters tall.

Part A:

Let's round each of the heights.

Mount Everest is 8,849.87 meters or approximately (I'm going to round to the nearest hundred) 8,800 meters.

Mount Olympus is 2,919.07 or approximately 2,900 meters.

Now, let's convert these numbers to scientific notation.

In order to convert a number to scientific notation, you would move the decimal to the left. Depending on how many spaces you move, you would then multiply the new number by 10 to the power of n.

Also, the new number must be between 1 and 10.

Mount Olympus is approximately 2,900.00 meters. To get a number between 1 and 10, we move the decimal place to the left three times. So:

`O=2.91907* 10^3`

Since we moved three times, we multiply by 10 to the third:

`O=2.9* 10^3`

Similarly for Mount Everest, it is approximately 8,800 meters. We are again going to move the decimal point to the left three times. So:

`E=8.8* 10^3`

To find how many times Everest is taller than Olympus, divide the two, with Everest in the numerator:

`(8.8* 10^3)/(2.9* 10^3)`

The 10 cubed will cancel. So:

`=(8.8)/(2.9)`

Divide. Use a calculator:

`\approx3`

So, Everest is approximately three times as tall as Olympus.

Part B)

Now, do the same instead this time, we won't round.

Olympus:

`O=2,919.07`

Move decimal three times to the left:

`O=2.91907* 10^3`

Same for Everest:

`E=8,849.87\\E=8.84987* 10^3`

Again, divide them:

`(8.84987* 10^3)/(2.91907* 10^3)`

Time 10 cubed cancel. Use a calculator:

`=(8.84987)/(2.91907)\approx3.031742987\approx3`

Again, this is approximately 3.

Part C:

Yes, we can. The estimate we got (when rounding to the nearest hundred) is extremely close to the value we acquired when we didn't round (3.0317). Therefore, we can conclude that our estimate in Part A is reasonable.

Answer 2

Explanation:

Part A:

Mount Everest Great Himalayas of southern Asia 8,849.87 meters

In scientific notation

8.84987 * 10 ^3

Rounding to the nearest whole number

9 * 10 ^3

Mount Olympus Mytikas, Greece 2,919.07 meters

In scientific notation

2.91907 * 10 ^3

Rounding to the nearest whole number

3 * 10 ^3

Taking Everest and diving by Olympus

9 * 10 ^3÷3 * 10 ^3 = 9/3 * 10 ^ (3-3) = 3

3 times

Part B:

Mount Everest Great Himalayas of southern Asia 8,849.87 meters

In scientific notation

8.84987 * 10 ^3

Mount Olympus Mytikas, Greece 2,919.07 meters

In scientific notation

2.91907 * 10 ^3

Taking Everest and diving by Olympus

8.84987 * 10 ^3÷2.91907 * 10 ^3

8.84987/2.91907 * 10^(3-3) = 3.031742987

Part C:

The estimate is reasonable. The estimate of 3 is very close to the value of 3.031742987 Therefore, we can conclude that the estimates for the heights were accurate.