To express the amount $15,528.23 in the form of \( a \times 10^n \), where \( a \) is a single digit, we first need to convert \( 15,528.23 \) into that format.
-
Identify \( a \) and \( n \):
- We start by expressing \( 15,528.23 \) in scientific notation. We need to find \( a \) as a single digit and \( n \) as an exponent of 10.
-
Move the decimal point to create a number between 1 and 10:
- Shifting the decimal point 1 position to the left gives us: \[ 1.552823 \]
- This shows that \( a = 1.552823 \).
-
The corresponding exponent \( n \) becomes:
- Since we moved the decimal point one position to the left from \( 15,528.23 \), we have: \[ n = 4 \]
-
Now, we ensure \( a \) is a single digit:
- We want to express it also in a form that \( a \) is truly a single digit. To do this, we can round: \[ a = 1.6 \quad (when , rounded) \]
-
Therefore, combining these gives us: \[ 15,528.23 \approx 1.6 \times 10^4 \]
Thus, the value of \( 15,528.23 \) in the form of \( a \times 10^n \) is \( \boxed{1.6 \times 10^4} \).