To solve the problem, let's break it down into two parts:
### Part (a): Approximate the depth of Challenger Deep by rounding to the nearest ten thousand feet.
1. Identify the depth of Challenger Deep:
The depth is given as 36,200 feet.
2. Determine the nearest ten thousand feet:
To round 36,200 to the nearest ten thousand, we need to look at the thousand's place (the third digit from the right). Here, the number is 6.
3. Apply the rounding rule:
- If the digit in the thousand's place is 5 or greater, we round up.
- If it is less than 5, we round down.
Since the digit is 6, which is greater than 5, we round up.
4. Perform the rounding:
Rounding 36,200 up to the nearest ten thousand feet, we get 40,000 feet.
Thus, the approximate depth of Challenger Deep rounded to the nearest ten thousand feet is 40,000 feet.
### Part (b): Write your answer from part (a) as a single digit times a power of 10 in exponential form.
1. Identify the rounded depth:
From part (a), we have 40,000 feet.
2. Express the number in exponential form:
- 40,000 can be expressed as 4 times 10,000.
- 10,000 itself can be written as [tex]\(10^4\)[/tex] in exponential form.
3. Combine the base and the exponent:
Therefore, 40,000 can be written as [tex]\(4 \times 10^4\)[/tex].
Putting this into a single digit times a power of 10 in exponential form, we have [tex]\(\mathbf{4 \times 10^4}\)[/tex].
### Summary:
- The approximate depth of Challenger Deep, rounded to the nearest ten thousand feet, is 40,000 feet.
- This depth, written as a single digit times a power of 10 in exponential form, is [tex]\(\mathbf{4 \times 10^4}\)[/tex].
