Question
COMPLETE Answerts a decimal. \( 2.8+7 . \overline{2}=\square \) DONE
Ask by Gross Frank. in the United States
Feb 06,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( 2.8 + 7.\overline{2} = 10.022222\ldots \)
Solution
To solve the expression \( 2.8 + 7.\overline{2} \):
1. **Understand the Notation:**
- The decimal \( 7.\overline{2} \) represents a repeating decimal, which is \( 7.2222\ldots \).
2. **Perform the Addition:**
\[
2.8 + 7.2222\ldots = 10.0222\ldots
\]
3. **Express as a Decimal:**
- The result is a repeating decimal \( 10.0222\ldots \).
**Final Answer:**
\[
10.022222\ldots
\]
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Simplify this solution The Deep Dive
To solve \( 2.8 + 7.\overline{2} \), we first convert \( 7.\overline{2} \) into a decimal. The repeating decimal \( 7.\overline{2} \) can be expressed as \( 7 + \frac{2}{9} \), which is approximately \( 7.2222... \). Now, adding \( 2.8 \) to \( 7.2222... \): \[ 2.8 + 7.2222... = 10.0222... \] Thus, \( 2.8 + 7.\overline{2} = 10.\overline{0}2 \), which is equivalent to approximately \( 10.022 \) in decimal form. So, our final answer is: \( 10.\overline{0}2 \) or simply \( 10.02 \).
