Chapter OneReal Number
Mathematics is originated from the process of expressing quantities in symbols or
numbers. The history of numbers is as ancient as the history of human civilization.
Greek Philosopher Aristotle According to the formal inauguration of mathematics occurs
in the practice of mathematics by the sect of priest in ancient Egypt. So, the number
based mathematics is the creation of about two thousand years before the birth of Christ.
After that, moving from many nations and civilization, numbers and principles of
numbers have gained an universal form at present.
The mathematicians in India first introduce zero (0) and 10 based place value system for
counting natural numbers, which is considered a milestone in describing numbers.
Chinese and Indian mathematicians extended the idea zero, real numbers, negative
number, integer and fractional numbers which the Arabian mathematicians accepted in
the middle age. But the credit of expressing number through decimal fraction is awarded
to the Muslim Mathematicians. Again they introduce first the irrational numbers in
square root form as a solution of the quadratic equation in algebra in the 11th century.
According to the historians, very near to 50 BC the Greek Philosophers also felt the
necessity of irrational number for drawing geometric figures, especially for the square
root of 2. In the 19th century European Mathematicians gave the real numbers a
complete shape by systematization. For daily necessity, a student must have a vivid
knowledge about ‘Real Numbers’. In this chapter real numbers are discussed in detail.
At the end of this chapter, the students will be able to –
¾ Classify real numbers
¾ Express real numbers into decimal and determine approximate value
¾ Explain the classification of decimal fractions
¾ Explain recurring decimal numbers and express fractions into recurring decimal
numbers
¾ Transform recurring decimal fraction into simple fractions
¾ Explain non-terminating non-recurring decimal fraction
¾ Explain non-similar and similar decimal fraction
¾ Add, subtract multiply and divide the recuring decimal fraction and solve various
problems related to them.