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

Question

where a
is single digit.(1 point)

Answer 1

To express the amount \(15,528.23\) in the form \(a \times 10^n\) where \(a\) is a single digit, we first need to identify appropriate values for \(a\) and \(n\).

1. We note that \( 15,528.23 \) can be rewritten by moving the decimal point one place to the left: \[ 15,528.23 = 1.552823 \times 10^4 \]

2. Now, we have \(a = 1.552823\) and \(n = 4\).

3. However, to express \( a \) as a single digit, we will round \( 1.552823 \) to the nearest place value: \[ a \approx 2 \quad (\text{since } 1.552823 \text{ rounds up to } 2) \]

4. Thus, we can express the amount as: \[ 2 \times 10^4 \]

Therefore, \(15,528.23\) in the form \(a \times 10^n\) where \(a\) is a single digit is:

\[ \boxed{2 \times 10^4} \]

Answer 2

u sure

Answer 3

Let's carefully review the conversion of \(15,528.23\) into the desired format of \(a \times 10^n\) with \(a\) as a single digit.

1. The original number is \(15,528.23\).

2. We want to express this in scientific notation, which typically involves moving the decimal point to the left until only one non-zero digit remains to its left.

   Moving the decimal point one place to the left gives us: \[ 1.552823 \times 10^4 \] where \(n = 4\).

3. However, for our requirement of \(a\) being a single digit, we need to round \(1.552823\):

   • The digit after the first digit (5) indicates we should round up.
   • Thus, \(1.552823\) rounds to \(2\).

4. Therefore, the scientific notation of \(15,528.23\) can be expressed as: \[ 2 \times 10^4 \]

So, after re-evaluating, my original answer remains correct. The correct expression is indeed: \[ \boxed{2 \times 10^4} \]