Real numbers are the universal language of mathematics, covering all kinds of numberical values that you can imagine – from integers to fractions, irrational numbers, prime numbers, and more.
Just picture a line that stretches on forever in both directions, every point on this line represents a real number. These includes numerical values like -1, 0, and 1, as well as larger values like 1000 and smaller values like 0.003 too.
Real numbers include fractions like 0.5, π = 3.14159, or even square root 2 = 1.41421356237.
Rational & Irrational Numbers
Let’s break it down further. But first, watch this video to better understand the differences.
Real numbers can be divided into two main categories: rational and irrational numbers.
Rational numbers can be written as fractions a/b , where a and b are integers and b is not equal to 0 (e.g., 0.5, -0.32, 3.4242424). They either end or eventually, start to repeat their decimal parts.
On the other hand, irrational numbers are numbers whose decimals are non-terminating and non-repeating. This means that the decimals will go on forever without settling into a repeating pattern. Examples of include π = 3.14159, square root 3 = 2.71828182846, and square root 5 = 2.2360679775.
Integers
Rational numbers can be further categorised into two subcategories: Integers and Fractions.
Integers are whole numbers, which are not fractions, and they can be positive or negative.
Fun Fact: Zero (0) is also considered a whole number!
Other examples include 1, 2, -1, and -2. Of which, 1 and 2 are considered positive integers while -1 and -2 are considered negative integers.
Natural numbers can also be further divided into three main types: the number one (1) itself, composite numbers, and prime numbers.
Composite numbers have more than two factors and can be divided by numbers other than 1 and themselves. Examples include 4, 6, 12 and 20.
Prime numbers, on the other hand, have exactly two factors (1 and itself) and cannot be divided evenly by any other number. Examples include 2, 3, 5 and 7.
Fractions
Fractions can be classified into two types based on their decimal representation: recurring decimals and terminating decimals.
Recurring decimals have a digit or group of digits that repeat indefinitely, such as 0.3 (which is written as 0.333…). Terminating decimals, on the other hand, have a finite number of digits after the decimal point and do not repeat indefinitely. Examples include 0.125, 0.3, and 9.57.
There are two types of fractions: recurring decimals and terminating decimals.
If a decimal has a digit or group of digits that repeats (e.g., 0.3, 9.25), then it is considered a recurring decimal.
On the other hand, terminating decimals have a finite number of decimal places. In other words, these end after a fixed number of digits after the decimal point. Examples of such decimals are 0.125, 0.3, 9.57.
Solving Questions using the Order of Operation Framework
Understanding the order of operations is important in maths to ensure precise calculations. To standardise this process, BODMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction) provides a clear framework for solving numerical expressions consistently, so as to navigate the complexities of mathematical computations.
Application Questions
Now that you have a firm grasp of real numbers and how to perform accurate calculations using the BODMAS framework, let’s put your skills to the test!
Checkpoint! Answer the following questions.
The table below shows the temperature of four cities at noon on a particular day in December.
| Singapore | 27°C |
| Shanghai | 4.6°C |
| Hong Kong | 16.3°C |
| Mongolia | -21.6°C |
- Find the difference in temperature between Singapore and Mongolia.
- Find the average temperature of the 4 cities.
- The temperature in Saudi Arabia is midway between the temperature in Shanghai and Hong Kong. What is the temperature in Saudi Arabia?
- If the temperature in Shanghai drops by 5.5°C one month later, find Shanghai’s temperature in one month’s time.
Check your answers! Did you get it right?
Want to Learn More?
Understanding the fundamentals of real numbers and mastering the BODMAS framework are essential skills that you need to solve maths problems with precision and confidence.
Still want more? Join our interactive live teaching sessions, where we delve into various concepts crucial for mastering the GCE O Level Elementary Mathematics exams.
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