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×10n where a is single digit.(1 p

Answer 1

To express the amount $15,528.23 in the form \( a \times 10^n \), we first convert the number into scientific notation.

1. Identify \( a \): We write \( 15,528.23 \) as \( 1.552823 \times 10^4 \) because we move the decimal point four places to the left.

2. Round \( a \): We round \( 1.552823 \) to one significant figure:

   • The first digit is 1. Since the next digit (5) is 5 or greater, we round up, giving us \( 2 \).

Thus, the rounded value of \( a \) is 2.

3. Determine \( n \): Since we moved the decimal point four places to the left, \( n = 4 \).

Putting it all together, we express \( 15,528.23 \) in the form \( a \times 10^n \): \[ 15,528.23 \approx 2 \times 10^4 \]

So the final answer is \( 2 \times 10^4 \).