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 \times 10^n where a is single digit. (1 point)

Answer 1

To express the amount \( 15,528.23 \) in the form of \( a \times 10^n \), we first need to find \( a \) (a single digit) and \( n \) (the exponent).

We can rewrite \( 15,528.23 \) as follows:

\[ 15,528.23 = 1.552823 \times 10^4 \]

Here, \( a = 1.552823 \) which has more than one digit. To express \( 15,528.23 \) as a single digit, we can round \( 1.552823 \) to a single digit, specifically rounding to the nearest tenths place which gives us \( 1.6 \).

Thus, adjusting \( n \) accordingly:

\[ 15,528.23 \approx 1.6 \times 10^4 \]

So the amount \( 15,528.23 \) expressed in the form of \( a \times 10^n \) where \( a \) is a single digit is:

\[ \boxed{1.6 \times 10^4} \]