Density of Rationals
Density of rational numbers means that between any two rational numbers, there are infinitely many rational numbers.
Practice This ConceptMain explanation
Teacher explanation
No two rational numbers are immediate neighbours. If two rational numbers are given, their average is one rational number between them, and the process can be repeated again and again.
Example
Between 1/3 and 1/2, one rational number is their average: (1/3 + 1/2)/2 = 5/12.
Simple analogy
There is always room between rationals.
Common confusion
Students often find only one rational number and think there are no more between the given numbers.
Exam tip
To find one rational number between two rationals, use the average method; to find many, make denominators same and insert numerators.
Study the density of rationals diagram carefully
Use the labelled diagram to keep density of rationals clear in short answers and revision.
What this diagram makes clear
This diagram keeps the labels and direction of density of rationals in the right order.
Where this helps in exams
Use this for labelled diagram work and short exam answers on density of rationals.
Revision cue
Revise density of rationals through the labels before writing the answer.
Answer writing and exam use
1-mark use
Write the exact meaning of density of rationals in one clean line.
2-mark use
Define density of rationals and add one example or condition.
3-mark use
Explain density of rationals, 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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