Math / Numbers & Operations

QuestionMount Everest, at 29,028 feet, is the tallest mountain on the Earth. What is its height in kilometers? Use unit analysis to answer this question. Round your answer to two decimal places.
Mount Everest is $\square$ km high.

Studdy Solution

STEP 1

What is this asking? We need to convert the height of Mount Everest from feet to kilometers. Watch out! Don't mix up conversion factors!
Make sure your units cancel correctly.

STEP 2

1. Gather conversion factors
2. Set up the conversion
3. Calculate the result

STEP 3

We know that there are approximately 12 inches in 1 foot, 5280 feet in 1 mile, and 1.60934 kilometers in 1 mile.
Let's write these down!

STEP 4

$1 \text{ foot} = 12 \text{ inches}$ $1 \text{ mile} = 5280 \text{ feet}$ $1 \text{ mile} = 1.60934 \text{ kilometers}$

STEP 5

We're starting with $\text{29,028 feet}$ .
We want to end up with $\text{kilometers}$ .
We'll multiply by fractions equal to one, but with different units, to make the units cancel out correctly.
It's like magic!

STEP 6

We can write the conversion as follows: $\text{29,028 feet} \cdot \frac{1 \text{ mile}}{5280 \text{ feet}} \cdot \frac{1.60934 \text{ kilometers}}{1 \text{ mile}}$

STEP 7

Notice how the units of $\text{feet}$ and $\text{miles}$ appear in both the numerator and denominator.
This is how we know we've set it up correctly!
They'll divide to one, and we'll be left with just $\text{kilometers}$ .

STEP 8

Let's do the math!
First, we'll divide $\text{29,028}$ by $\text{5280}$ : $\frac{29028}{5280} \approx 5.497727$

STEP 9

Now, we'll multiply the result by $\text{1.60934}$ : $5.497727 \cdot 1.60934 \approx 8.84784$

STEP 10

The problem asks us to round to two decimal places.
Looking at the third decimal place, which is $7$ , we round up.

STEP 11

So, our final answer is approximately $8.85$ kilometers.

STEP 12

Mount Everest is $8.85$ km high.

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QuestionMount Everest, at 29,028 feet, is the tallest mountain on the Earth. What is its height in kilometers? Use unit analysis to answer this question. Round your answer to two decimal places.
Mount Everest is $\square$ km high.

Studdy Solution

STEP 1

What is this asking? We need to convert the height of Mount Everest from feet to kilometers. Watch out! Don't mix up conversion factors!
Make sure your units cancel correctly.

STEP 2

1. Gather conversion factors
2. Set up the conversion
3. Calculate the result

STEP 3

We know that there are approximately 12 inches in 1 foot, 5280 feet in 1 mile, and 1.60934 kilometers in 1 mile.
Let's write these down!

STEP 4

$1 \text{ foot} = 12 \text{ inches}$ $1 \text{ mile} = 5280 \text{ feet}$ $1 \text{ mile} = 1.60934 \text{ kilometers}$

STEP 5

We're starting with $\text{29,028 feet}$ .
We want to end up with $\text{kilometers}$ .
We'll multiply by fractions equal to one, but with different units, to make the units cancel out correctly.
It's like magic!

STEP 6

We can write the conversion as follows: $\text{29,028 feet} \cdot \frac{1 \text{ mile}}{5280 \text{ feet}} \cdot \frac{1.60934 \text{ kilometers}}{1 \text{ mile}}$

STEP 7

Notice how the units of $\text{feet}$ and $\text{miles}$ appear in both the numerator and denominator.
This is how we know we've set it up correctly!
They'll divide to one, and we'll be left with just $\text{kilometers}$ .

STEP 8

Let's do the math!
First, we'll divide $\text{29,028}$ by $\text{5280}$ : $\frac{29028}{5280} \approx 5.497727$

STEP 9

Now, we'll multiply the result by $\text{1.60934}$ : $5.497727 \cdot 1.60934 \approx 8.84784$

STEP 10

The problem asks us to round to two decimal places.
Looking at the third decimal place, which is $7$ , we round up.

STEP 11

So, our final answer is approximately $8.85$ kilometers.

STEP 12

Mount Everest is $8.85$ km high.

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QuestionMount Everest, at 29,028 feet, is the tallest mountain on the Earth. What is its height in kilometers? Use unit analysis to answer this question. Round your answer to two decimal places.Mount Everest is □\square□ km high.

Studdy Solution

STEP 1

What is this asking? We need to convert the height of Mount Everest from feet to kilometers. Watch out! Don't mix up conversion factors!Make sure your units cancel correctly.

STEP 2

1. Gather conversion factors2. Set up the conversion3. Calculate the result

STEP 3

We know that there are approximately **12 inches** in **1 foot**, **5280 feet** in **1 mile**, and **1.60934 kilometers** in **1 mile**.Let's write these down!

STEP 4

1 foot=12 inches 1 \text{ foot} = 12 \text{ inches} 1 foot=12 inches 1 mile=5280 feet 1 \text{ mile} = 5280 \text{ feet} 1 mile=5280 feet 1 mile=1.60934 kilometers 1 \text{ mile} = 1.60934 \text{ kilometers} 1 mile=1.60934 kilometers

STEP 5

We're starting with 29,028 feet\text{29,028 feet}29,028 feet.We want to end up with kilometers\text{kilometers}kilometers.We'll multiply by fractions equal to one, but with different units, to make the units cancel out correctly.It's like magic!

STEP 6

We can write the conversion as follows: 29,028 feet⋅1 mile5280 feet⋅1.60934 kilometers1 mile \text{29,028 feet} \cdot \frac{1 \text{ mile}}{5280 \text{ feet}} \cdot \frac{1.60934 \text{ kilometers}}{1 \text{ mile}} 29,028 feet⋅5280 feet1 mile​⋅1 mile1.60934 kilometers​

STEP 7

Notice how the units of feet\text{feet}feet and miles\text{miles}miles appear in both the numerator and denominator.This is how we know we've set it up correctly!They'll divide to one, and we'll be left with just kilometers\text{kilometers}kilometers.

STEP 8

Let's do the math!First, we'll divide 29,028\text{29,028}29,028 by 5280\text{5280}5280: 290285280≈5.497727 \frac{29028}{5280} \approx 5.497727 528029028​≈5.497727

STEP 9

Now, we'll multiply the result by 1.60934\text{1.60934}1.60934: 5.497727⋅1.60934≈8.84784 5.497727 \cdot 1.60934 \approx 8.84784 5.497727⋅1.60934≈8.84784

STEP 10

The problem asks us to round to two decimal places.Looking at the third decimal place, which is 777, we round up.

STEP 11

So, our **final answer** is approximately 8.858.858.85 kilometers.

STEP 12

Mount Everest is 8.858.858.85 km high.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionMount Everest, at 29,028 feet, is the tallest mountain on the Earth. What is its height in kilometers? Use unit analysis to answer this question. Round your answer to two decimal places.
Mount Everest is $\square$ km high.

What is this asking? We need to convert the height of Mount Everest from feet to kilometers. Watch out! Don't mix up conversion factors!
Make sure your units cancel correctly.

1. Gather conversion factors
2. Set up the conversion
3. Calculate the result

We know that there are approximately 12 inches in 1 foot, 5280 feet in 1 mile, and 1.60934 kilometers in 1 mile.
Let's write these down!

$1 \text{ foot} = 12 \text{ inches}$ $1 \text{ mile} = 5280 \text{ feet}$ $1 \text{ mile} = 1.60934 \text{ kilometers}$

We're starting with $\text{29,028 feet}$ .
We want to end up with $\text{kilometers}$ .
We'll multiply by fractions equal to one, but with different units, to make the units cancel out correctly.
It's like magic!

We can write the conversion as follows: $\text{29,028 feet} \cdot \frac{1 \text{ mile}}{5280 \text{ feet}} \cdot \frac{1.60934 \text{ kilometers}}{1 \text{ mile}}$

Notice how the units of $\text{feet}$ and $\text{miles}$ appear in both the numerator and denominator.
This is how we know we've set it up correctly!
They'll divide to one, and we'll be left with just $\text{kilometers}$ .

Let's do the math!
First, we'll divide $\text{29,028}$ by $\text{5280}$ : $\frac{29028}{5280} \approx 5.497727$

Now, we'll multiply the result by $\text{1.60934}$ : $5.497727 \cdot 1.60934 \approx 8.84784$

The problem asks us to round to two decimal places.
Looking at the third decimal place, which is $7$ , we round up.

So, our final answer is approximately $8.85$ kilometers.

Mount Everest is $8.85$ km high.