Question
Rounding to the leftmost digit, calculate the approximate value for the following expressions. \( \begin{array}{llll}\text { a. } 879 & \text { b. } 1788 & \text { c. } 178 \cdot 975 & \text { d. } 78,719+75\end{array} \) a. Using leftmost digit rounding, the sum is approximately \( \square \).
Ask by Fernandez Martin. in the United States
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Using leftmost digit rounding, \(879\) is approximately \(900\).
Solution
1. Identify the leftmost digit of \(879\).
The leftmost digit is \(8\) in the hundreds place.
2. Determine the place value of the leftmost digit:
Since \(8\) is in the hundreds place, we will round \(879\) to the nearest hundred.
3. Look at the next digit (the tens digit) to decide on rounding:
The tens digit is \(7\).
Since \(7 \geq 5\), we round up the leftmost digit.
4. Increase the leftmost digit by 1:
\(8 + 1 = 9\).
5. Replace all other digits with zeros, maintaining the same place value:
The rounded value is \(900\).
Thus, using leftmost digit rounding, the approximate value of \(879\) is \(900\).
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Simplify this solution Extra Insights
To round to the leftmost digit, we focus on the first significant figure in each number. For \( 879 \), the leftmost digit is \( 8 \), and since there's a \( 7 \) following it, we round up to get approximately \( 900 \). For \( 1788 \), the leftmost digit is \( 1 \), but there’s a \( 7 \) right next to it, so we round up to approximately \( 2000 \). Now for \( 178 \cdot 975 \), we can round them to \( 200 \) and \( 1000 \) respectively, giving us \( 200 \cdot 1000 \approx 200000 \). Lastly, for \( 78,719 + 75 \), rounding to leftmost gives us \( 80,000 + 100 \approx 80,000 \). So, the approximate values would be: a. \( 900 \) b. \( 2000 \) c. \( 200000 \) d. \( 80000 \)
