Real Numbers And Their Decimal Expansions
Chapter Name : Number Systems |
Sub Topic Code : 104_09_01_03_01 |
Topic Name : Real Numbers And Their Decimal Expansions |
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Sub Topic Name : Real Numbers And Their Decimal Expansions |
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Introduction
Decimal expansion of a real number.
Pre-Requisites:
Basic knowledge of real numbers and division.
Activity:
Write down an irrational number in decimal form and observe that the decimal form is non-recurring and non-terminating.
Real Life Question:
If a cake is cut into 3 equal pieces then how much is each piece in the form of a rational number and in decimal form? Is it a terminating decimal? If it is cut into 4 equal pieces, then how does the answer change?
Key Words / FlashCards
| Key Words | Definitions (pref. in our own words) |
|---|---|
| Rational number Recurring decimals Terminating decimals Irrational number Real numbers | Any number which can be written in p/q form, q ?0 is called rational number. A decimal number of the form a.bcdebcdebcde… i.e., the numbers in the decimal is repeating. A decimal number in which ends with a finite number of decimal digits. Any number which cannot be written in the form of p/q, where q?0 is called as irrational number Collections of rational and irrational numbers is called as real numbers |
Learning aids / Gadgets
| Gadgets | How it can be used |
|---|---|
| Rational numbers and irrational numbers chart and decimal forms | Write randomly few rational numbers and irrational form and find their decimal forms. What can you conclude? |
Real life uses :
Consider fencing a circular plot, the perimeter is an irrational number, but it is normally approximated to a rational number.
Practical examples around us
| Examples | Explainations |
|---|---|
| A farmer had a circular plot of radius 7m; he said the area to be 154 m2. Is that right? | Not exactly, here the farmer approximated ? to be 22/7 but ??22/7.But can be approximated to 22/7. |
What you learn in Theory:
Rational numbers and irrational numbers decimal notation.
What you learn in Practice:
Terminating and recurring decimals and how we can identify a number is rational or irrational number