What you’ll learn
Locate irrational numbers on number line.
Key idea
Compare exact squared tick values with the radicand; strict bounds exclude both endpoints.
Approximate bounding ticks are not the exact irrational point; count indices from the actual origin.
Worked example
Enter the exact value or ordered values in the format requested below.
A number line starts at 4 (index zero) and has ticks every 0.1, ending at 5. Enter the tick label immediately left of exact point √20.
- Exact squared tick bounds give 4.4²<20<4.5², so 4.4<√20<4.5.
- On a tenth line starting at 4, left label 4.4 has index (4.4-4)/0.1=4.
- Strict inequalities place the irrational point between ticks, not exactly at a bounding tick.
Answer: 4.4
Quick Check
Evaluate a worked attempt at locate irrational numbers on number line, identify the first invalid step, and provide the correction.
A number line starts at 6 (index zero) and has ticks every 0.1, ending at 7. Step 1 establishes 6.8²<47<6.9². Step 2 plots √47 exactly on tick 6.9. Locate the first invalid step and correct the placement.