Pi (π)
In short: Pi is the fixed ratio obtained by dividing the distance around any circle by the distance across it, a number close to 3.14159 that no fraction matches exactly.
7th GradeGeometry7.G.B.4
What is Pi?
Pi appears when you measure around a wheel, then across it, and divide the first number by the second: the answer lands a bit above 3. Repeat with a coin or a table and the quotient hardly moves, and that unchanging quotient is written \(\pi\).
In symbols, \(\pi = \frac{C}{d}\) for every circle. Its decimal form, 3.14159265 and onward, never ends and never repeats, so no fraction equals the constant exactly. The values 3.14 and \(\frac{22}{7}\) are handy stand-ins, not the number itself.
How to spot it
- A circle appears and the wording brings up circumference, area or roundness.
- An answer is requested “in terms of \(\pi\)”, like 20π square feet.
- The task says to use 3.14 or the calculator key for the constant.
- You hold two measurements of a round object, around and across, and must compare them.
The method
- Measure the distance around the circle and the distance across it through the center.
- Divide the first by the second; the quotient lands near 3.14 for every circle.
- While computing, keep the symbol \(\pi\) until the last step, or swap in 3.14 if the problem allows rounding.
- Say whether the final answer is exact, like \(36\pi\), or approximate, like 113.1.
Pi: solved example
Problem
A tailor measures a round tablecloth: 188.5 centimeters around the edge and 60 centimeters across. What ratio does this give, and how near is it to the famous constant?
Solution
Divide the distance around by the distance across: \(\frac{188.5}{60} \approx 3.1417\).
That sits within about 0.0001 of 3.14159, so the ratio is approximately 3.14; the tiny gap comes from rounding the measurements.
Try it
Question 1
Taking 3.14 for the constant, find the circumference of a dinner plate 9 inches wide.
Show the answer
\(3.14 \times 9 = 28.26\) inches.
Question 2
Does \(\frac{22}{7}\) equal π exactly?
Show the answer
No. \(\frac{22}{7} = 3.142857…\), a little larger than π, and its digits repeat while the digits of π do not.
Pi vs. Circumference
The constant is one fixed number, identical for all circles. A circumference is a length that depends on the circle’s size and equals that constant times the diameter. A tiny ring and a stadium track share the same ratio but have very different edge lengths.
Keep going
Lessons
Worksheets and quizzes
Related words
Whole dictionary: A–Z · 7th Grade · Geometry