Rational Numbers
A rational number is any number that can be written as p/q, where p and q are integers and q is not zero.
Practice This ConceptMain explanation
Teacher explanation
Rational numbers include integers, fractions, terminating decimals, and non-terminating repeating decimals. They can be represented on the number line by dividing the space between integers into equal parts.
Example
-3, 0, 4/7, 2.5, and 0.333... are rational numbers because each can be written as p/q with q not equal to zero.
Simple analogy
Rational means ratio-ready.
Common confusion
Students sometimes think only positive fractions are rational, but negative fractions and integers are rational too.
Exam tip
For number-line questions, first locate the two nearest integers and then divide the interval according to the denominator.
Study the rational numbers diagram carefully
Use the labelled diagram to keep rational numbers clear in short answers and revision.
What this diagram makes clear
This diagram keeps the labels and direction of rational numbers in the right order.
Where this helps in exams
Use this for labelled diagram work and short exam answers on rational numbers.
Revision cue
Revise rational numbers through the labels before writing the answer.
Answer writing and exam use
1-mark use
Write the exact meaning of rational numbers in one clean line.
2-mark use
Define rational numbers and add one example or condition.
3-mark use
Explain rational numbers, show the method or example, and mention the common mistake.
Practice this concept with focused MCQs
Open the concept quiz intro first, review the test details, and then start a focused MCQ set from this concept only. Instant score and answer review are live now.
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