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This is the Cambridge International Examinations Mathematics textbook. It is a free textbook for revision.
CAMBRIDGE
Cambridge University Press
978-1-107-60988-4 - Cambridge IGCSE Core Mathematics
Karen Morrison and Lucille Dunne
Excerpt
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Reviewing number concepts
1.1 Different types of numbers
- Real numbers can be divided into rational and irrational numbers. You will deal with rational numbers in this chapter. Irrational numbers are covered in chapter 9.
- Rational numbers can be written as fractions in the form of $\frac{a}{b}$ where $a$ and $b$ are integers and $b \neq 0$. (Integers are negative and positive whole numbers, and zero.)
- Integers, fractions and terminating decimals are all rational numbers.
Tip
Make sure you know what the following sets of numbers are: natural numbers, integers, odd and even numbers and prime numbers.
Exercise 1.1
1 Copy and complete this table by writing a definition and giving an example of each type of number.
Mathematical name | Definition | Example
Natural numbers | &
Integers | &
Prime numbers | &
Square numbers | &
Fraction | &
Decimal | &
2 Include numbers to show what each of the following symbols means. For example $100>99$.
(a) $>$
(b) $\leq$
(c) $\approx$
(d) $\therefore$
(e) $\sqrt{ }$
(f) $\neq$
(g) $\geq$
(h) <
3 Look at this set of numbers.
\[
3,-2,0,1,9,15,4,5,-7,10,32,-32,21,23,25,27,29, \frac{1}{2}
\]
(a) Which of these numbers are NOT natural numbers?
(b) Which of these numbers are NOT integers?
(c) Which of these numbers are prime numbers?
(d) Which of these numbers are square numbers?
4 List:
(a) four square numbers greater than 100 .
(b) four rational numbers smaller than $\frac{1}{3}$.
(c) two prime numbers that are $>80$.
(d) the prime numbers $<10$.
Unit 1: Number
1
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