Pi
Pi is the ratio of any circle's circumference to its diameter, approximately equal to 3.14. In Grade 6 Saxon Math Course 1 (Chapter 5: Number and Operations), students learn that for every circle, the circumference is always about 3.14 times the diameter: C = pi x d. Pi is an irrational number whose decimal expansion never ends or repeats. Students use pi approximately equal to 3.14 for calculations. A circle with diameter 10 cm has circumference approximately 3.14 x 10 = 31.4 cm. Pi also appears in the area formula A = pi x r squared, connecting circumference and area.
Key Concepts
Property The exact number of diameters in a circumference is represented by the Greek letter $\pi$. We use the approximation $\pi \approx 3.14$.
Examples A plate with a circumference of 78 cm and a diameter of 25 cm has a ratio of $\frac{78}{25} \approx 3.12$. A trash can with a circumference of 122 cm and a diameter of 38 cm has a ratio of $\frac{122}{38} \approx 3.21$. For any perfect circle, the ratio of its circumference (C) to its diameter (d) is exactly $\pi$: $\frac{C}{d} = \pi$.
Explanation Pi is the ultimate magic number for any circle! Imagine you measure a circle's distance around (circumference) and divide it by the distance across (diameter)—you always get pi. It's a super long, never ending decimal, so we just call it $\pi$ and use 3.14 as a handy shortcut. It’s the secret ingredient for all circle related math!
Common Questions
What is pi in mathematics?
Pi is the ratio of a circle's circumference to its diameter, approximately 3.14159... For Grade 6 calculations, use pi approximately equal to 3.14 or 22/7.
Is pi rational or irrational?
Pi is irrational. Its decimal expansion never ends and never repeats: 3.14159265358979...
How is pi used to find circumference?
Use C = pi x d (diameter) or C = 2 x pi x r (radius). Multiply 3.14 by the diameter, or by twice the radius.
A circle has diameter 20 cm. What is its circumference?
C = 3.14 x 20 = 62.8 cm.
How can you verify that pi is approximately 3.14?
Measure any circular object's circumference and diameter, then divide circumference by diameter. The result will always be close to 3.14.