## Approximations of Irrational Numbers

#### Aligned To Common Core Standard:

**Grade 8 Number System** - 8.NS.A.2

How to make Approximations of 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: r^0 = 3 r^1 = 3.1 = 31/10 r^2 = 3.14 = 314/100 r^3 = 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: r^0 = 1 r^1 = 1.4 = 14/10 r^2 = 1.41 = 141/100 r^3 = 1.414 = 1414/1000 This is will go on with the same frequency as the approximation of π. These worksheets and lessons help students learn how to convert irrational numbers to the more understandable rational form.

### Printable Worksheets And Lessons

- Comparing Radicals
Step-by-Step Lesson- Use a numbers line to compare radicals
of five and seven.

- Guided Lesson -
Approximate the value of radical numbers to the nearest tenth.

- Guided Lesson Explanation
- We use numbers lines again to help us visualize where the values
lie.

- Independent Practice
- Approximate values for five problems and compare radicals for
another five problems.

- Matching Worksheet
- Sorry that we ended up with an odd number of problems on the this
one. I know it makes it tougher to grade.

- Approximations of Irrational Numbers Five Pack - You are basically simplifying these irrational statements.

#### Homework Sheets

Point out the approximation of the value of irrational numbers.

- Homework 1 - Compare √10 and √12.
- Homework 2 - Because we only need to go to the tenths place, we could work from a list of the possible multiples.
- Homework 3 - Find the approximation of √150 to the nearest tenth.

#### Practice Worksheets

More approximations. These make great in-class activities.

- Practice 1 - Compare √55 and √57.
- Practice 2 - How do these two stack up?
- Practice 3 - Wonderdog goes after it.

#### Math Skill Quizzes

The quizzes also include operations with irrational integers.