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Chapter 5: Problem 104

Choose the best estimate. \(1.437+20.69\) a. 34 b. 22 c. 3.4 d. 2.2

Short Answer

Expert verified
Option b. 22 is the best estimate.

Step by step solution

01

Analyze the problem

We need to find an approximate value for the sum of two decimals: \(1.437 + 20.69\). This means we need to estimate the sum without calculating the exact value.
02

Round the numbers

Start by rounding each number to the nearest whole number to make estimation easier. \(1.437\) rounds to \(1\), and \(20.69\) rounds to \(21\).
03

Estimate the sum

Add the rounded numbers to estimate the sum: \(1 + 21 = 22\).
04

Choose the best estimate

Compare the estimated sum of \(22\) with the options provided. The correct choice should be the one closest to our estimate of \(22\).

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Key Concepts

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

Rounding Numbers
Understanding rounding is fundamental in estimation. It involves adjusting a number to its nearest simple value, like a whole number, making calculations easier to handle.

For instance, when rounding a decimal to the nearest whole number, you look at the first decimal digit:
  • If it's 5 or higher, you round up the whole number.
  • If it's 4 or lower, you round down.
In the exercise, we took the decimal 1.437 and rounded it to 1 because 4 is less than 5. Similarly, 20.69 was rounded to 21 because 6 is more than 5. This simplification helps when estimating sums.
Adding Decimals
Adding decimals may seem tricky, but it's straightforward with a bit of practice. Key things to remember include:
  • Align the decimal points vertically when adding multiple numbers.
  • Add each column starting from the rightmost digit and move left.
When estimating, however, it is often unnecessary to add the decimals precisely. Instead, rounding them as shown in the exercise simplifies addition, making mental math easier. The exercise demonstrated this by turning decimals into whole numbers for an estimated sum.
Mathematics Problem-Solving
Problem-solving in mathematics involves several strategic steps. Understanding what the problem asks for is the first step before proceeding with operations.

In the provided exercise, solving the problem required:
  • Identifying that the task was to estimate, not find the exact sum.
  • Rounding each number to its nearest whole number, to simplify the process.
  • Adding the rounded values to provide a quick and practical solution.
This approach teaches how breaking down a complex task into simpler steps facilitates efficient and accurate problem-solving.
Approximation Skills
Approximation is a valuable skill in everyday mathematical tasks. It involves estimating a value that is close to the exact answer. This skill is useful when precision is less important or when quick decisions need to be made.

In the exercise:
  • We approximated the decimal numbers into whole numbers.
  • Quickly added them to get an estimated total.
  • Compared the estimate with available multiple-choice answers.
Developing approximation skills helps in making faster calculations and also enhances decision-making efficiency in mathematical practices.

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