Estimate Large and Small Quantities Practice

Question

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Question
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
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 need to write it in scientific notation.

1. Start with the number: \( 15,528.23 \).
2. Move the decimal point to create a number between 1 and 10. This means moving the decimal point 1 place to the left, resulting in \( 1.552823 \).
3. Now, we count how many places we moved the decimal point. We moved it 1 place, so we will multiply by \( 10^4 \) (because \( 10^4 = 10,000 \)) to adjust for this.

Putting it all together, we get: \[ 15,528.23 = 1.552823 \times 10^4 \] However, since we need to express \( a \) as a single digit, we can round \( 1.552823 \) to \( 2 \) (following normal rounding rules).

Thus, \( 15,528.23 \) can be rounded further to: \[ = 1.6 \times 10^4 \] So, our final answer in the form \( a \times 10^n \) is: \[ 1.6 \times 10^4 \] with \( a = 1.6 \) and \( n = 4 \).