Irrational Numbers
Chapter Name : Number Systems |
Sub Topic Code : 104_09_01_02_01 |
Topic Name : Irrational Numbers |
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Sub Topic Name : Irrational Numbers |
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Introduction
What is an irrational number?
Pre-Requisites:
Basic knowledge about Pythagorean theorem and irrational numbers
Activity:
Take scale, pencil, protractor to draw right angled triangles with two of its lengths being (1,1), ( ?2,1),(1,2) and measure the lengths of the hypotenuse. You will observe the hypotenuse lengths being ?2, ?3 , ?5.
Real Life Question:
An ant wanted to crawl from A to C in ABCD rectangular room of dimension 2m*1m.How could the ant travel with covering minimum distance. What is that length?
Key Words / FlashCards
| Key Words | Definitions (pref. in our own words) |
|---|---|
| irrational number Rational Numbers Real numbers | Any number which cannot be written in the form of p/q, where q?0 is called as irrational number The numbers which can be written in p/q form, q? 0, p, q are integers. Collections of rational and irrational numbers is called as real numbers |
Learning aids / Gadgets
| Gadgets | How it can be used |
|---|---|
| Right angled triangles to know about irrational numbers | Draw 1*1 rt angled triangle to get ?2.Similarly take ?2 and 1 to get the length ?3, and do for ?5 and ?7. |
Real life uses :
Distance of the hypotenuse in an isosceles rt angled triangle is always an irrational number.
Practical examples around us
| Examples | Explainations |
|---|---|
| If a bullock cart is moving at 0.5 rev/sec with a wheel of 1m radius, what is the distance travelled in 10sec? | 0.5*2?*1 m/sec = ? m/sec. Therefore in 10sec = 10 ?m. Which is an irrational number. |
What you learn in Theory:
Irrational numbers, representation of irrational numbers on number line, Real numbers.
What you learn in Practice:
How to draw a length of an irrational number using rt angled triangles