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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

a
×
10
n
where a
a
is single digit.

3 answers

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

  1. Start with the number \( 15,528.23 \).

  2. Move the decimal point to the left until we only have one non-zero digit to the left of the decimal. In this case, we move the decimal point 1 place to the left to get \( 1.552823 \).

  3. So, we can express \( 15,528.23 \) as \( 1.552823 \times 10^4 \).

  4. We round \( 1.552823 \) to the nearest place value, which is the nearest hundredth (or two decimal places). This means we round \( 1.552823 \) to \( 1.55 \).

Putting this together, we have: \[ 15,528.23 \approx 1.55 \times 10^4 \]

Thus, in the form \( a \times 10^n \):

  • \( a = 1.55 \)
  • \( n = 4 \)

So the final answer is: \[ 1.55 \times 10^4 \]

no. you have to round it, so the answer is 2*10^4, but you were closer than I was. I appreciate your help

Thank you for your understanding, and I appreciate your clarification!

You're correct that rounding \( 1.552823 \) to the nearest whole number gives \( 2 \). Therefore, the representation of \( 15,528.23 \) in the form \( a \times 10^n \) after rounding should indeed be:

\[ 2 \times 10^4 \]

Thank you for pointing that out! If you have any further questions or need more assistance, feel free to ask!