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It takes 10 years for a $100 monthly bank deposit to amount to $15,528.23 when invested at 5% interest compounded monthly. Round to the nearest place value, then express the amount $15,528.23 in the form of 𝑎 × 10^𝑛 where 𝑎 is single digit.

To express the amount $15,528.23 in the form of \( a \times 10^n \), we need to round $15,528.23 to the nearest significant figure and format it accordingly.

1. **Identifying \( a \)**: The leading digit in $15,528.23 is 1.
2. **Finding \( n \)**: To write it in scientific notation, we count how many places we move the decimal point to get from 15,528.23 to 1.552823. We move it 4 places to the left.

Thus, we can express $15,528.23 as:

\[
1.552823 \times 10^4
\]

Now, rounding \( a \) to one significant figure:

\[
1.552823 \approx 2 \quad (\text{rounded to one significant figure})
\]

So, the final result in the form of \( a \times 10^n \) is:

\[
2 \times 10^4
\]

Therefore, \( a = 2 \) and \( n = 4 \).

it says I got it wrong

Let’s carefully break down the problem step by step to accurately convert \( 15,528.23 \) into the proper scientific notation format.

1. **Identify the significant figures**: We want to express \( 15,528.23 \) in the format \( a \times 10^n \) where \( a \) is a single-digit number.

2. **Convert to scientific notation**:
- Move the decimal point in \( 15,528.23 \) to the left until only one non-zero digit is to the left of the decimal point.
- Moving the decimal point from the end of \( 15,528.23 \) four places to the left gives us \( 1.552823 \).

3. **Count how many places we moved the decimal point**:
- We moved it 4 places to the left, which means we have \( n = 4 \).

4. **Express in scientific notation**:
- So, \( 15,528.23 \) can initially be written as \( 1.552823 \times 10^4 \).

5. **Rounding to the required format**:
- We need \( a \) to be a single-digit number. The initial \( 1.552823 \) is valid, but in scientific notation for just one significant figure, we need to round \( 1.552823 \) to \( 2 \).

Thus, when rounding to one significant figure, we get:

\[
2 \times 10^4
\]

This means:
- \( a = 2 \)
- \( n = 4 \)

If you’re looking precisely for \( 15,528.23 \) itself, without rounding \( a \), the correct expression would be:

\[
1.5528 \times 10^4
\]

But if \( a \) must strictly be one digit then \( 2 \times 10^4 \) is indeed the proper representation.

If the answer was deemed incorrect, please check the specific formatting or requirements provided, just to ensure compliance with the guidelines given to you.

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