Question
it takes 10 years for 100 monthly bank deposit to amount to 15,528 and $.23 when invested at 5% interest compounded a monthly round to the nearest place value then express the amount 15,528 and $.23 in the form of a times 10 to the power of N where a is a single digit
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Answered by
GPT-4o mini
To express the amount $15,528.23 in the form of \( a \times 10^N \), where \( a \) is a single digit, we need to adjust the number accordingly:
1. Identify the significant digit:
- The first digit is \( 1 \).
2. Count the number of places we move the decimal point to express it in scientific notation:
- Move the decimal 4 places to the left, which gives us \( 1.552823 \).
So, we express \( 15,528.23 \) as:
\[
1.552823 \times 10^4
\]
However, since we need \( a \) to be a single digit, we can express \( 15,528.23 \) in the form of:
\[
1.6 \times 10^4
\]
Rounded to one decimal place.
Thus, the final answer in scientific notation is:
\[
1.6 \times 10^4
\]
1. Identify the significant digit:
- The first digit is \( 1 \).
2. Count the number of places we move the decimal point to express it in scientific notation:
- Move the decimal 4 places to the left, which gives us \( 1.552823 \).
So, we express \( 15,528.23 \) as:
\[
1.552823 \times 10^4
\]
However, since we need \( a \) to be a single digit, we can express \( 15,528.23 \) in the form of:
\[
1.6 \times 10^4
\]
Rounded to one decimal place.
Thus, the final answer in scientific notation is:
\[
1.6 \times 10^4
\]
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