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Pi

Study Guide

Key Definition

Pi, represented as $\pi$, is the ratio of a circle's circumference to its diameter.

Important Notes

  • Pi, $\pi$, is an irrational number.
  • Common approximations: $\frac{22}{7}$ and $3.14$.
  • Pi is constant for all circles.
  • Pi cannot be precisely expressed as a fraction.
  • The first few digits of $\pi$ are 3.14159.

Mathematical Notation

$\pi$ represents the ratio of circumference to diameter$\frac{C}{d}$ is the formula for PiRemember to use proper notation when solving problems

Why It Works

Pi is derived from the consistent ratio of circumference to diameter across all circles, represented as $\frac{C}{d} = \pi$.

Remember

The value of $\pi$ starts with 3.14159, and it never repeats or terminates.

Quick Reference

Pi Formula:$\pi = \frac{C}{d}$

Understanding Pi

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Video explanation of this concept

concept. Use space or enter to play video.concept thumbnailBeginner

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Beginner Explanation

Pi is the ratio of a circle's circumference to its diameter: $\pi = \frac{C}{d}$.Now showing Beginner level explanation.

Practice Problems

Test your understanding with practice problems

1

Quick Quiz

Single Choice QuizBeginner

What is the value of $\pi$ to two decimal places?

A$3.14$B$3.15$C$3.13$D$3.16$Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.2

Real-World Problem

Question ExerciseIntermediate

Teenager Scenario

You are designing a circular garden. If the diameter of the garden is 10 meters, what is the circumference using $\pi \approx 3.14$?Show AnswerClick to reveal the detailed solution for this question exercise.3

Thinking Challenge

Thinking ExerciseIntermediate

Think About This

Why can't $\pi$ be exactly represented as a fraction?

Show AnswerClick to reveal the detailed explanation for this thinking exercise.4

Challenge Quiz

Single Choice QuizAdvanced

Which of the following is a correct approximation of $\pi$ to four decimal places?

A$3.1416$B$3.1415$C$3.1420$D$3.1400$Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.

Recap

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Review key concepts and takeaways

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