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1 month ago
1 month ago
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 π Γ 10^π where π is single digit.
1 month ago
To express the amount $15,528.23 in the form of \( a \times 10^n \), we need to round $15,528.23 to the nearest significant figure and format it accordingly.
1. **Identifying \( a \)**: The leading digit in $15,528.23 is 1.
2. **Finding \( n \)**: To write it in scientific notation, we count how many places we move the decimal point to get from 15,528.23 to 1.552823. We move it 4 places to the left.
Thus, we can express $15,528.23 as:
\[
1.552823 \times 10^4
\]
Now, rounding \( a \) to one significant figure:
\[
1.552823 \approx 2 \quad (\text{rounded to one significant figure})
\]
So, the final result in the form of \( a \times 10^n \) is:
\[
2 \times 10^4
\]
Therefore, \( a = 2 \) and \( n = 4 \).
1 month ago
it says I got it wrong
1 month ago
Letβs carefully break down the problem step by step to accurately convert \( 15,528.23 \) into the proper scientific notation format.
1. **Identify the significant figures**: We want to express \( 15,528.23 \) in the format \( a \times 10^n \) where \( a \) is a single-digit number.
2. **Convert to scientific notation**:
- Move the decimal point in \( 15,528.23 \) to the left until only one non-zero digit is to the left of the decimal point.
- Moving the decimal point from the end of \( 15,528.23 \) four places to the left gives us \( 1.552823 \).
3. **Count how many places we moved the decimal point**:
- We moved it 4 places to the left, which means we have \( n = 4 \).
4. **Express in scientific notation**:
- So, \( 15,528.23 \) can initially be written as \( 1.552823 \times 10^4 \).
5. **Rounding to the required format**:
- We need \( a \) to be a single-digit number. The initial \( 1.552823 \) is valid, but in scientific notation for just one significant figure, we need to round \( 1.552823 \) to \( 2 \).
Thus, when rounding to one significant figure, we get:
\[
2 \times 10^4
\]
This means:
- \( a = 2 \)
- \( n = 4 \)
If youβre looking precisely for \( 15,528.23 \) itself, without rounding \( a \), the correct expression would be:
\[
1.5528 \times 10^4
\]
But if \( a \) must strictly be one digit then \( 2 \times 10^4 \) is indeed the proper representation.
If the answer was deemed incorrect, please check the specific formatting or requirements provided, just to ensure compliance with the guidelines given to you.
1 month ago
thank you bye
1 month ago