The Decimal Expansion of π

Examples, solutions, and videos to help Grade 8 students learn how to calculate the decimal expansion of π using basic properties of area and estimate the value of expressions such as π².

New York State Common Core Math Grade 8, Module 7, Lesson 14

Worksheets for Grade 8

Lesson 14 Student Outcomes • Students calculate the decimal expansion of π using basic properties of area.
• Students estimate the value of expressions such as π².

Lesson 14 Summary

Irrational numbers, such as π, are frequently approximated in order to compute with them. Common approximations for π are 22/7 and 3.14. It should be understood that using an approximate value of an irrational number for computations produces an answer that is accurate to only the first few decimal digits.

Lesson 14 Classwork

Opening Exercises

1. Write an equation for the area, A, of the circle shown.
2. Write an equation for the circumference, C, of the circle shown.
3. Each of the squares in the grid below has an area of 1 unit².
   a. Estimate the area of the circle shown by counting squares.
   b. Calculate the area of the circle using a radius of 5 units and 3.14 for π.

Exercises
4. Gerald and Sarah are building a wheel with a radius of 6.5 cm and are trying to determine the circumference. Gerald says, “Because 6.5 × 2 × 3.14 = 40.82, the circumference is 40.82 cm.” Sarah says, “Because 6.5 × 2 × 3.10 = 40.3 and 6.5 × 2 × 3.21 = 41.73, the circumference is somewhere between 40.3 and 41.73.” Explain the thinking of each student.
5. Estimate the value of the irrational number (6.12486…)².
6. Estimate the value of the irrational number (9.204107…)².
6. Estimate the value of the irrational number (4.014325…)².

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