Which of the following is the best order of magnitude estimate in meters of the height of a mountain?

a) 1 m
b) 10 m
c) 100 m
d) 1000 m

And your thinking is...?

We will be happy to critique your thinking or work.

I perosnally think that it is d is that correct?

As an order of magnitude, it is probably the best. 1000m can mean 500 m to 5000m

1000

For Problems 13 and 14, make a magnitude estimate. Circle the appropriate box. Then solve each problem. Show your work.

1000m

Well, I must say, that's quite the mountain of options you've got there! But fear not, for I, the mighty Clown Bot, am here to guide you through this treacherous terrain.

Now, when it comes to estimating the height of a mountain, we're looking for an order of magnitude, which basically means a rough approximation. So let's put on our "guestimation" hats and explore your options.

A) 1 meter: Well, that seems rather short for a mountain, unless you're talking about a molehill. So, let's move on, shall we?

B) 10 meters: Ah, now we're getting somewhere. But still, 10 meters might be more suitable for a tree or a tall building rather than a mountain. Onward we go!

C) 100 meters: Now, we're starting to hit the sweet spot! Think of this as the elevation of a small hill, rather than a grand mountain. So, close but no cigar.

D) 1000 meters: Ah, the mighty option D! Now we're talking! This order of magnitude estimate seems to be the most fitting for the height of a proper mountain. It's not too small like the previous options, and it's not too big to make us believe we're talking about Mount Everest. Huzzah!

So, my dear friend, it seems your instincts are right on the money! Option D, 1000 meters, appears to be the best order of magnitude estimate for the height of a mountain. Clap clap for you!

To determine the best order of magnitude estimate for the height of a mountain, we need to consider the typical height range for mountains.

A reasonable range for the height of mountains is generally between a few hundred meters to several thousand meters.

Option a) 1m is too small to be an accurate estimate for the height of a mountain.

Option b) 10m is also too small and falls within the range of hills rather than mountains.

Option c) 100m is a bit closer to the height of a small mountain, but it is still on the lower end of the range and may be more suitable for hills or smaller geological formations.

Option d) 1000m falls within the typical range for mountains and is considered a more accurate estimate for the height.

Keep in mind that this is an order of magnitude estimate, meaning it provides a rough approximation that can vary by a factor of 10 in either direction. The actual height of mountains can vary greatly, so it's important to consider the context and specific location when making more precise estimations.

In conclusion, option d) 1000m is the best order of magnitude estimate for the height of a mountain.