Q1 of 114 Page 35

Define (i) rational numbers

A rational number is any number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non - zero denominator q.


(ii) irrational numbers


An irrational number is a number that cannot be expressed as a fraction p/q for any integers p and q. Irrational numbers have decimal expansions that neither terminate nor become periodic


(iii) real numbers.


Real numbers are numbers that can be found on the number line. This includes both the rational and irrational numbers.


More from this chapter

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2

Without actual division, show that each of the following rational numbers is a non-terminating repeating decimal.

i. ii.


iii. iv.


v. vi.


vii. viii.

3

Express each of the following as a fraction in simplest form.

i. ii.


iii. iv.


v. vi.

2

Classify the following numbers as rational or irrational:

i. ii. 3.1416


iii. π iv.


v. 5.636363 … vi. 2.040040004 …


vii. 1.535335333 … viii. 3.121221222 …


ix.

3

Prove that each of the following numbers is irrational.

i. ii.


iii. iv.


v. vi.


vii. viii.


xi.