How do I solve Number System problems?

Rational numbers can be expressed as p/q where q ≠ 0. Their decimal form either terminates or repeats. Irrational numbers cannot be expressed as p/q. Their decimal form is non-terminating and non-repeating (e.g., √2, π).

What are common mistakes in Number System?

Claiming that √4 is irrational (it equals 2, which is rational). Confusing non-terminating repeating decimals (rational) with non-terminating non-repeating decimals (irrational).

Which class covers Number System?

Number System is typically taught in Class 9. SparkEd has free practice for all these grades.

Where can I practise Number System for free?

SparkEd offers free chapter-wise practice for Number System aligned to CBSE, ICSE, and IB curricula. Visit sparkedmaths.com to start.

How to Solve Number System — Step by Step Guide

Rational, irrational numbers and their representation on the number line. This guide covers Class 9 to 9.

Step-by-Step Method

1
Rational numbers can be expressed as p/q where q ≠ 0. Their decimal form either terminates or repeats.
2
Irrational numbers cannot be expressed as p/q. Their decimal form is non-terminating and non-repeating (e.g., √2, π).
3
To represent √n on the number line: use the spiral of Theodorus or the Pythagoras method.
4
Rationalise the denominator by multiplying by the conjugate: 1/√a = √a/a.
5
Laws of radicals: √a × √b = √(ab), √a / √b = √(a/b), (√a)² = a.

Worked Example

Problem: Rationalise the denominator of 1/√3.

Solution: 1/√3 × √3/√3 = √3/3.

Common Mistakes to Avoid

✗
Claiming that √4 is irrational (it equals 2, which is rational).
✗
Confusing non-terminating repeating decimals (rational) with non-terminating non-repeating decimals (irrational).
✗
Forgetting to rationalise the denominator when simplifying expressions.
✗
Incorrect simplification of nested radicals.

Practice Number System on SparkEd

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CBSE Class 9 Number Systems

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Frequently Asked Questions

How do I solve Number System problems?: Rational numbers can be expressed as p/q where q ≠ 0. Their decimal form either terminates or repeats. Irrational numbers cannot be expressed as p/q. Their decimal form is non-terminating and non-repeating (e.g., √2, π).
What are common mistakes in Number System?: Claiming that √4 is irrational (it equals 2, which is rational). Confusing non-terminating repeating decimals (rational) with non-terminating non-repeating decimals (irrational).
Which class covers Number System?: Number System is typically taught in Class 9. SparkEd has free practice for all these grades.
Where can I practise Number System for free?: SparkEd offers free chapter-wise practice for Number System aligned to CBSE, ICSE, and IB curricula. Visit sparkedmaths.com to start.

SparkEd Maths — sparked.coms@gmail.com — www.sparkedmaths.com