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Chapter 1: Problem 9

Estimate each sum by rounding. Then find the actual sum. $$43,210+135,569+2088+516$$

Short Answer

Expert verified
Answer: The estimated sum is 181,500 and the actual sum is 181,383.

Step by step solution

01

Round each number

To estimate the sum, we must first round each number: $$43,210 \approx 43,000$$ $$135,569 \approx 136,000$$ $$2088 \approx 2000$$ $$516 \approx 500$$
02

Add the rounded numbers together

Now that we have rounded each number, we can add them together for an estimated total: $$43,000 + 136,000 + 2,000 + 500 = 181,500$$
03

Add the actual numbers together

Now that we have an estimated sum, let's find the actual sum by adding the exact numbers together: $$43,210 + 135,569 + 2088 + 516 = 181,383$$ The estimated sum is 181,500 and the actual sum is 181,383.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Rounding Numbers
Rounding numbers is a useful skill that helps simplify complex calculations. It involves adjusting a number to the nearest defined place value.
This makes computation quicker and often still accurate enough for many practical purposes.
  • For example, the number 43,210 rounded to the nearest thousand is 43,000. The "2" in the hundreds place is less than five, so the thousands digit remains the same.
  • On the other hand, 135,569 becomes 136,000 when rounded to the nearest thousand. Here, the "5" in the hundreds place causes the thousands digit to round up.
When rounding numbers, always consider place value and whether the digit you're rounding from is five or higher, as this will determine if you round up or down. This concept is pivotal when estimating sums quickly.
Actual Sum
The actual sum is the real total you get when you add numbers without any rounding. It gives the precise result of an addition problem.
  • In our example, we directly add 43,210, 135,569, 2088, and 516 together to get 181,383.
  • This method ensures that we account for every unit within each number, providing an accurate solution.
Using the actual sum is crucial when exact results are necessary, such as in financial statements or scientific calculations.
It鈥檚 important to practice adding numbers precisely to improve your math skills and accuracy.
Addition
Addition is one of the fundamental operations in mathematics, allowing us to combine amounts to find a total. Understanding how to add different types of numbers is essential.
Here are some basics:
  • Align numbers by their rightmost digits when writing them down for addition. This helps avoid mistakes.
  • Start adding from the rightmost column (units) and move left, carrying over any values as needed.
  • For a problem like 43,210 and 135,569, first add the units column, then tens, moving leftwards, keeping track of any carryovers.
Building a strong foundation in addition helps not just in math, but in everyday life scenarios like budgeting or calculating totals.
Estimation Techniques
Estimation techniques help us to quickly approximate the sum of numbers without needing exact figures.
They are particularly useful in scenarios where time is of essence, or an approximated value is sufficient.
  • Rounding is one common method, as seen in our example where each number is rounded before summing. This gives us a quick estimate of 181,500.
  • Another technique is using benchmarks鈥攙alues we already know鈥攖o gauge where the sum might fall, such as estimating 2088 as around 2000.
By using estimation techniques, you can make quick decisions or checks, ensuring efficiency in both academic and real-world problem-solving.

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Most popular questions from this chapter

Simplify. Show your steps. $$9 \cdot 4-24 \div 4 \cdot 2-6$$

Simplify. Show your steps. $$9(2 \cdot 7-6 \cdot 2)$$

The following table shows the ACT scores of a group of students applying to a college. Find the mean, median, and mode score. $$\begin{array}{l|c|l|c}\hline \text { Student } & \text { ACT score } & \text { Student } & \text { ACT score } \\ \hline \text { Barnes, K. } & 31 & \text { Johnson, E. } & 28 \\ \hline \text { Compton, S. } & 28 & \text { Milton, C. } & 25 \\ \hline \text { Donaldson, R. } & 34 & \text { Nelson, D. } & 24 \\\ \hline \text { Garcia, J. } & 29 & \text { Robinson, W. } & 21 \\ \hline \text { Hamilton, S. } & 25 & \text { Stevenson, L. } & 25 \\ \hline \text { James, T. } & 21 & \text { Wilson, B. } & 21 \\ \hline\end{array}$$

Simplify. Show your steps. $$54 \div 2+\\{15-3[20 \div(4+6)]\\}$$

Simplify. Show your steps. $$36-3^{2} \cdot 4+14$$
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