Question
What is \( 790 \frac{20}{65} \) rounded to the nearest hundred?
Ask by Turnbull Erickson. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( 790 \frac{20}{65} \) rounded to the nearest hundred is 800.
Solution
To round \( 790 \frac{20}{65} \) to the nearest hundred, follow these steps:
1. **Interpret the Mixed Number**:
- \( 790 \frac{20}{65} \) is a mixed number, which means it's equivalent to \( 790 + \frac{20}{65} \).
2. **Simplify the Fraction**:
- \( \frac{20}{65} \) can be simplified by dividing both the numerator and the denominator by 5:
\[
\frac{20 \div 5}{65 \div 5} = \frac{4}{13} \approx 0.3077
\]
3. **Combine the Whole Number and the Fraction**:
- \( 790 + 0.3077 \approx 790.3077 \)
4. **Round to the Nearest Hundred**:
- To round to the nearest hundred, look at the digit in the tens place.
- Here, \( 790.3077 \) is closer to \( 800 \) than to \( 700 \).
Therefore, \( 790 \frac{20}{65} \) rounded to the nearest hundred is **800**.
**Answer:**
800
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Simplify this solution Bonus Knowledge
To round \( 790 \frac{20}{65} \) to the nearest hundred, first, convert the fraction to a decimal. The fraction \( \frac{20}{65} \) simplifies to approximately \( 0.3077 \). So, the expression can be rewritten as \( 790 + 0.3077 \), which equals approximately \( 790.3077 \). When rounding \( 790.3077 \) to the nearest hundred, we look at the hundreds place (which is 7 in 700). Since we have 790, we consider the next digit (the tens place), which is a 9. As 9 is greater than 5, we round up. Therefore, \( 790 \frac{20}{65} \) rounded to the nearest hundred is \( 800 \).
