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Chapter 1: Problem 12

In Exercises 9-22, obtain an estimate for each computation by rounding the numbers so that the resulting arithmetic can easily be performed by hand or in your head. Then use a calculator to perform the computation. How reasonable is your estimate when compared to the actual answer? \(7.92+3.06+24.36\)

Short Answer

Expert verified
Estimate: 35, Actual Computation: 35.34. The estimate is reasonable as it is quite close to the actual value.

Step by step solution

01

Rounding the numbers

The first step is to round the numbers to the nearest whole number which makes the calculation easier to do by hand or in the head. Thus, the numbers \(7.92\), \(3.06\), and \(24.36\) are rounded to \(8\), \(3\), and \(24\) respectively.
02

Estimation

The second step is to add these rounded numbers together and the result obtained forms the estimate. Therefore, \(8+3+24 = 35\).
03

Actual Computation

The third step is to use a calculator to add the original numbers together: thus, \(7.92 + 3.06 + 24.36 = 35.34\).

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Key Concepts

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

Rounding Numbers
Rounding numbers means simplifying digits to make calculations easier. When you round, you adjust the numbers up or down to a nearby, more convenient number. This is typically done to the nearest whole number or another specified decimal place. In our example, the numbers were rounded as follows:
  • 7.92 becomes 8.
  • 3.06 becomes 3.
  • 24.36 becomes 24.
Rounding helps in quick calculations by removing complex decimal places. It's especially useful in mental arithmetic, where precision may be less important than speed and simplicity.
Calculator Usage
Using a calculator ensures that arithmetic operations are accurate and precise, especially when dealing with decimal numbers. While estimation gives us a good understanding of what the answer should look like, the calculator provides the exact result. In our example, using a calculator to add the numbers 7.92, 3.06, and 24.36 gives an accurate sum of 35.34. This allows us to see how close our rounded estimate was to the actual result. Even in a world with calculators readily accessible, understanding the basics of estimation and rounding builds foundational arithmetic skills.
Whole Numbers
Whole numbers are integers that do not have fractional or decimal components. By converting numbers to whole ones, we simplify arithmetic and can focus on easy addition, subtraction, multiplication, or division. In practical terms, whole numbers are vital in estimation, as they make it easier to handle operations mentally. In the example, rounding transformed 7.92 to 8, 3.06 to 3, and 24.36 to 24. All of these are whole numbers that make calculation simpler without detracting too much from accuracy.
Arithmetic Estimation
Arithmetic estimation is the process of deducing a rough calculation to understand the likely results without needing an exact calculation. It's a useful skill for making fast decisions and checking work. For example, in the exercise, rounding each number to the closest whole number gave us an estimated sum of 35. Knowing the final calculator result as 35.34 helps confirm the estimate was reasonable and close enough for an initial guess. Estimation helps in everyday tasks such as budgeting and quick mental calculations, making it a valuable tool.

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Most popular questions from this chapter

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