Veda Bites are swipeable micro-lessons — each one teaches exactly one
idea. Here's a taste from this kit; the app has the full deck.
💡 Key Idea
Rational vs Irrational: The Decimal Test
Decimals reveal a number's true identity.
Every real number is either rational or irrational — and the decimal expansion tells you which.
↳ If the decimal neither terminates nor repeats, the number is irrational — no exceptions.
📖 Definition
What Is a Rational Number?
Ratio of two integers — that's the whole story.
↳ The denominator q must never be zero — that single condition defines the set.
⭐ Important Fact
Infinitely Many Rationals Between Any Two
Squeeze a rational — there's always room.
Between any two rational numbers, there are infinitely many rational numbers — not just one.
↳ Density of rationals: no 'next' rational exists after any given one.
📖 Smart notes
What you'll study, topic by topic
1
Class IX Maths SA-1: Number Systems, Polynomials, Coordinate Geometry, Linear Equations & Lines and Angles
This SA-1 syllabus covers five core Class IX Maths units: number systems (rational vs irrational, decimal expansions, surds), polynomials (degree, zeros, factorisation, identities), coordinate geometry (quadrants, plotti…
A rational number can be written as $\frac{p}{q}$ where $p, q$ are integers and $q \ne 0$.
Irrational numbers have non-terminating, non-repeating decimal expansions.
$1.101001000100001\ldots$ is irrational because the pattern never repeats.
~20 min · full explanation, examples & memory tricks in the app
❓ Leveled MCQ practice
Try the smart MCQs from this kit
20 questions laddered from warm-up to topper-level, each with an explanation. A taste:
Which of the following is an example of an irrational number?
Beginner
A $\frac{3}{4}$B $1.101001000\ldots$C $0.75$D $0.\overline{6}$
Show answer & explanation
$1.101001000\ldots$
$1.101001000\ldots$ is non-terminating and non-repeating, so it is irrational. The others are terminating or repeating decimals, hence rational.
How many rational numbers lie between $\frac{1}{5}$ and $\frac{2}{5}$?
Beginner
A Exactly twoB Infinitely manyC Exactly oneD None
Show answer & explanation
Infinitely many
Between any two rational numbers there are infinitely many rational numbers.
What is the coefficient of $x$ in $9x^2 + 4x - 6$?
Beginner
A $2$B $6$C $9$D $4$
Show answer & explanation
$4$
The coefficient of $x$ is the number multiplying $x$, which is $4$.
The full Veda Bites deck, complete notes, spaced-repetition
flashcards, leveled MCQs, tests and games for this kit — plus
Daily Facts and the Arena, every day.