Explore the real number system, including rational and irrational numbers, and their representation on the number line.
Real numbers include all rational numbers (expressible as p/q) and irrational numbers (non-terminating, non-repeating decimals like โ2 and ฯ).
Is 0.333... (repeating) rational or irrational?
Rational, since it equals 1/3, expressible as p/q
Is โ5 rational or irrational?
Irrational, since 5 is not a perfect square
Both rational and irrational numbers can be represented precisely on the number line, with irrational numbers like โ2 located using geometric construction.
How can โ2 be located on the number line using a right triangle?
Construct a right triangle with legs 1 and 1; the hypotenuse has length โ2, which can be transferred to the number line using a compass
Between which two integers does โ10 lie?
3 and 4, since 3ยฒ=9<10<16=4ยฒ
1. Is 0.25 rational or irrational?
2. Is โ11 rational or irrational?
3. Between which two integers does โ20 lie?
4. Is 22/7 rational or irrational?
5. Simplify: โ18