Estimate Irrational Numbers Grade 8.pptx

Estimate Irrational Numbers

1. Estimating Irrational Numbers Reveal Math – Grade 9 | Topic 2-4

2. What Are Irrational Numbers? • Numbers that cannot be written as a fraction a/b. • Their decimal form is non-terminating and non-repeating. Examples: √2, π, √3, e.

3. Irrational vs Rational Numbers Rational: Can be written as a fraction or repeating decimal (e.g., 0.5, 1/3). Irrational: Cannot be written as a fraction (e.g., √5, π). Irrational numbers fill the gaps between rational numbers on the number line.

4. Why Estimate Irrational Numbers? Exact decimal values are infinite and non-repeating. We estimate to understand their approximate location on the number line. Example: √2 ≈ 1.414 → Between 1 and 2.

5. Using Perfect Squares to Estimate 1. Find two perfect squares between which the number lies. Example: √8 → between √4 = 2 and √9 = 3. 2. Estimate closer value: √8 ≈ 2.8.

6. Example 1 Estimate √50. Find perfect squares: 49 < 50 < 64 → √49 = 7, √64 = 8. So, √50 ≈ 7.1 (closer to 7).

7. Example 2 Estimate √20. Perfect squares: 16 < 20 < 25 → √16 = 4, √25 = 5. So, √20 ≈ 4.47 → about 4.5.

8. Locating on a Number Line Estimate √3 ≈ 1.7 → between 1 and 2. Estimate √10 ≈ 3.16 → between 3 and 4. Helps visualize where irrational numbers lie among rational ones.

9. Practice Time! Estimate the following irrational numbers: 1. √5 2. √12 3. √30 4. √80 Try using nearby perfect squares for each.

10. Reflection • Why is estimating irrational numbers useful? • How can you check if your estimate makes sense? • Remember: estimation gives a sense of size, not exactness!