# Approximations of Irrational Numbers Worksheets

How to Approximate Irrational Numbers? Decimal expansion of a rational number provides a similar sequence that comes through rational approximations. For example, the value of π is 3.14159… The approximation of π can be carried out through: r0 = 3, r1 = 3.1 = 31/10, r2 = 3.14 = 314/100, r3 = 3.141 = 3141/1000. These numbers give out a sequences and better approximation of the value of Pi. Similarly, √2 = 1.41421 which can be approximated by the rational number sequence: r0 = 1, r1 = 1.4 = 14/10, r2 = 1.41 = 141/100, r3 = 1.414 = 1414/1000 This is will go on with the same frequency as the approximation of π.

• ### Basic Lesson

Demonstrates how to approximate radicals and pi to the nearest tenth.

• ### Intermediate Lesson

Explores how to approximate radicals and pi to the nearest hundredth.

• ### Independent Practice 1

Contains 20 Approximations of Irrational Numbers problems. The answers can be found below.

• ### Independent Practice 2

Features another 20 Approximations of Irrational Numbers problems.

• ### Homework Worksheet

Approximations of Irrational Numbers problems for students to work on at home. Example problems are provided and explained.

• ### Topic Quiz

10 Approximations of Irrational Numbers problems. A math scoring matrix is included.

• ### Homework and Quiz Answer Key

Answers for the homework and quiz.

• ### Lesson and Practice Answer Key

Answers for both lessons and both practice sheets.

#### Cyclic Math Isn't Just Circles

142,857 is a cyclic number, the numbers of which always appear in the same order but rotated around when multiplied by any number from 1 to 6. 142,857 x 2 = 285,714 142,857 x 3 = 428,571 142,857 x 4 = 571,428 142,857 x 5 = 714,285 142,857 x 6 = 857,142 Source: Dave Pigott