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Chapter 0: Problem 19

Replace the question mark by \(<,>,\) or \(=\), whichever is correct. \(\pi ? 3.14\)

Short Answer

Expert verified
蟺 > 3.14

Step by step solution

01

Understand the symbols

The symbols to use are less than (<), greater than (>), or equal to (=). We need to determine which symbol correctly compares 蟺 (pi) and 3.14.
02

Know the value of 蟺

Recall that 蟺 is an irrational number approximately equal to 3.14159. This is an important piece of information for the comparison.
03

Compare 蟺 and 3.14

Since 蟺 is approximately 3.14159, and 3.14159 is greater than 3.14, it follows that 蟺 > 3.14.

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Key Concepts

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

Irrational Numbers
Irrational numbers are numbers that cannot be expressed as simple fractions. This means they have non-repeating, non-terminating decimal representations. For example, \(\frac{22}{7}\) is a rational approximation of 蟺, but it鈥檚 not exactly 蟺 since 蟺 cannot be expressed exactly as a fraction. Other common examples include \(\sqrt{2}\) and the mathematical constant e.
Inequalities
Inequalities are mathematical expressions that show the relationship between two values. The symbols used are less than (<), greater than (>), and equal to (=). Understanding inequalities is crucial in comparing numbers. For example, if we say \( 5 > 3 \), it means 5 is greater than 3. In the context of the exercise, we used inequalities to compare 蟺 and 3.14.
Value of Pi
Pi (蟺) is one of the most famous irrational numbers, used to represent the ratio of the circumference of a circle to its diameter. The value of 蟺 is approximately equal to 3.14159, but it cannot be represented exactly as it has an infinite number of decimal places. In our exercise, knowing that 蟺 is approximately 3.14159 helped us determine that 蟺 > 3.14 since 3.14159 is greater than 3.14.

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Most popular questions from this chapter

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