1. Ronald Hui Tak Sun Secondary School
Mathematics
Ronald Hui
Tak Sun Secondary School

2. Mathematics I am English teacher! Mathematics is an English lesson
We are English (EMI) School!!!
Ronald HUI

3. Mathematics What should be ready in the next lesson? Textbook
Erasable Pens
Notebook & folder
Ronald HUI

4. DSE Mathematics Further information Talk to me?
Talk to me?
Facebook: Ronald Hui
IG: ronaldhuisir
Whatsapp:
Homepage for F4 students:
Ronald HUI

5. Good Luck! Shall we start?
Ronald HUI
4 September 2017

6. Real Number System

7. Positive integers are also called natural numbers.
Positive integers, negative integers and zero together form the system of integers.
Integers
Negative integers
…, –4, –3, –2, –1,
Zero 0,
Positive integers
1, 2, 3, 4, …
Positive integers are also called natural numbers.

8. p and q are integers and q ≠ 0
Rational numbers
Rational numbers are numbers which can be
expressed as . p q
p and q are integers and q ≠ 0
Fractions and integers together form the system of rational numbers.
For example:
, , , 1 5 2 –9 17 4 3 1 1 –6 1
3 = , 0 = , –6 =
Integers
These are fractions.
Rational numbers
These are integers.
Fractions

9. By long division, all fractions can be converted into terminating decimals or recurring decimals.
Consider and
(i)
(ii) ∴ ∴

10. Can all terminating decimals and recurring decimals be converted into fractions?
For terminating decimal,
(i)
(ii)

11. All terminating decimals and recurring decimals are rational numbers.
For recurring decimal,
Let
i.e.
(2)  (1):
All terminating decimals and recurring decimals are rational numbers. ∴

12. p and q are integers and q ≠ 0
Irrational numbers
Irrational numbers are numbers which cannot be
expressed as . p q
p and q are integers and q ≠ 0
They can only be written as non-terminating and non-recurring decimals.
For example:

13. Real numbers
Rational and irrational numbers together form the real number system.
Real numbers
Rational numbers
Irrational numbers
, 
–4,
When plotting each real number above on a real number line, we have

14. Now, we summarize the relationships among different kinds of real numbers as follows:

15. Follow-up question Consider the following numbers. , 8, , , 3.5, 4
, 8, , , 3.5, 4
Rational numbers
Integer 8
Fraction
Terminating decimal
3.5
Recurring decimal
Irrational numbers
, 4