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 of $15,528.23 in the form of a×10^n

where a
is a single digit.

1 answer

To express the amount \(15,528.23\) in the form \(a \times 10^n\), we need to rewrite it in scientific notation.

The number \(15,528.23\) is between \(10,000\) and \(100,000\), so we can express it as follows:

  1. Move the decimal point to the left until there is only one non-zero digit to the left of the decimal point. This gives us \(1.552823\).
  2. Count how many places we moved the decimal point. Here, we moved it 4 places to the left.
  3. Therefore, we multiply \(1.552823\) by \(10^4\).

Thus, we can express \(15,528.23\) as: \[ 1.552823 \times 10^4 \]

To round \(1.552823\) to the nearest single digit, we look at the first digit after the decimal point which is \(5\). Since \(5\) is 5 or more, we round up:

\[ 1.552823 \rightarrow 2 \]

So rounded to the nearest single digit, we have \(2\).

Thus, the amount \(15,528.23\) can be expressed in scientific notation as:

\[ 2 \times 10^4 \]

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

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