Denali, which is about 20,000 ft above sea level, is the highest mountain in the United States. Mt. Everest, the highest mountain on Earth, is about $9 \times 10^3\text{ ft}$ higher than Denali. About how high is Mt. Everest? The answer should be in scientific notation.

A$1.1 \times 10^3\text{ ft}$
B$29,000\text{ ft}$
C$2.9 \times 10^3\text{ ft}$
D$2.9 \times 10^4\text{ ft}$

Question

03-11-2026
Mathematics

Answered

Denali, which is about 20,000 ft above sea level, is the highest mountain in the United States. Mt. Everest, the highest mountain on Earth, is about $9 \times 10^3\text{ ft}$ higher than Denali. About how high is Mt. Everest? The answer should be in scientific notation.

A$1.1 \times 10^3\text{ ft}$
B$29,000\text{ ft}$
C$2.9 \times 10^3\text{ ft}$
D$2.9 \times 10^4\text{ ft}$

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GinnyAnswer GinnyAnswer · Answer 1 · 2026-11-03T10:54:52-05:00

Convert the given heights to standard numerical form: Denali is $20,000$ ft and the difference is $9,000$ ft.
Sum these values to find the height of Mt. Everest: $20,000 + 9,000 = 29,000$ ft.
Express the result in scientific notation by moving the decimal point: $2.9 \times 10^4$ ft.
The final answer is $\boxed{2.9 \times 10^4 \text{ ft.}}$

Explanation

Analyzing the Problem

We are given that the height of Denali is approximately $20,000$ ft above sea level. Mt. Everest is known to be $9 \times 10^3$ ft higher than Denali. We need to calculate the height of Mt. Everest and express it in scientific notation. Scientific notation is a way of writing numbers that are too large or too small to be conveniently written in decimal form, represented as $a \times 10^n$, where $1 \le |a| < 10$ and $n$ is an integer.

Converting Values to Standard Form

First, let's represent the given heights in standard numerical form. The height of Denali is $20,000$ ft. The additional height of Mt. Everest compared to Denali is $9 \times 10^3$. Since $10^3 = 1,000$, we have $9 \times 1,000 = 9,000$. Therefore, the additional height is $9,000$ ft.

Calculating the Total Height and Converting to Scientific Notation

To find the total height of Mt. Everest, we add the height of Denali and the additional height:
\[20,000 + 9,000 = 29,000 \text{ ft}.\]
Now, we need to convert $29,000$ into scientific notation. We move the decimal point four places to the left to place it after the first digit (which is 2), giving us $2.9$. Since we moved the decimal point four places to the left, we multiply by $10^4$. Thus, the height of Mt. Everest is $2.9 \times 10^4$ ft.

Examples

Scientific notation is extremely useful in real-world applications involving very large or small numbers, such as astronomy or particle physics. For example, the distance from Earth to the Sun is about $1.496 \times 10^8$ km. By using scientific notation, scientists avoid long strings of zeros and can perform calculations more efficiently, reducing the risk of errors in complex scientific research.