Number Systems Formulas - Mathematics Class 9

Learn important formulas from the Number Systems chapter of Class 9 Mathematics with examples, variables and applications.

📐 Number Systems Formulas

Complete collection of formulas with explanations and examples

Power Law of Exponents

$$(a^m)^n = a^(mn)$$

Description: Power Law of Exponents is a standard relation used in number-systems.

Example:

Apply the relation: (a^m)^n = a^(mn)

Identify the known values, substitute them in the relation, and solve for the unknown quantity.
Result depends on the substituted values.

Applications:

  • Use this when the quantities in the relation are known and the missing quantity is required.

Product Law of Exponents

$$a^m x a^n = a^(m+n)$$

Description: Product Law of Exponents is a standard relation used in number-systems.

Example:

Apply the relation: a^m x a^n = a^(m+n)

Identify the known values, substitute them in the relation, and solve for the unknown quantity.
Result depends on the substituted values.

Applications:

  • Use this when the quantities in the relation are known and the missing quantity is required.

Quotient Law of Exponents

$$a^m / a^n = a^(m-n)$$

Description: Quotient Law of Exponents is a standard relation used in number-systems.

Example:

Apply the relation: a^m / a^n = a^(m-n)

Identify the known values, substitute them in the relation, and solve for the unknown quantity.
Result depends on the substituted values.

Applications:

  • Use this when the quantities in the relation are known and the missing quantity is required.

Rationalisation Conjugate

$$1/(a + sqrt(b)) = (a - sqrt(b))/(a^2 - b)$$

Description: Rationalisation Conjugate is a standard relation used in number-systems.

Example:

Apply the relation: 1/(a + sqrt(b)) = (a - sqrt(b))/(a^2 - b)

Identify the known values, substitute them in the relation, and solve for the unknown quantity.
Result depends on the substituted values.

Applications:

  • Use this when the quantities in the relation are known and the missing quantity is required.

Quick Reference

Power Law of Exponents: $(a^m)^n = a^(mn)$
Product Law of Exponents: $a^m x a^n = a^(m+n)$
Quotient Law of Exponents: $a^m / a^n = a^(m-n)$
Rationalisation Conjugate: $1/(a + sqrt(b)) = (a - sqrt(b))/(a^2 - b)$

💡 Worked Examples

Step-by-step solutions using Number Systems formulas

Example 1: Area of Circle

Circle Area Formula
Problem:

Find the area of a circle with radius 7 cm.

Solution:
  1. Given: r = 7 cm
  2. Apply formula: A = πr²
  3. Substitute: A = π × 7²
  4. Calculate: A = π × 49 = 49π cm²
  5. Approximate: A ≈ 49 × 3.14159 ≈ 153.94 cm²
Answer:

Area = 49π cm² ≈ 153.94 cm²

🎯 Practice Problems

Try these problems to test your understanding:

Practice Problem 1

Solve the quadratic equation: x² - 7x + 12 = 0

Practice Problem 2

Find the area of a circle with diameter 14 cm.

Practice Problems

Check Your Formula Recall

Write each formula once, define every variable, then solve one direct substitution problem before moving to mixed questions.

Apply Number Systems

Pick two formulas from this page and create your own values for the variables. Verify units and signs before calculating.

Derivation Notes

Focus on how the formula is built, not only the final expression. Derivations help with board-exam reasoning and multi-step application questions.

  • Start from the definition or identity used in the chapter.
  • Write assumptions clearly before substituting values.
  • Track units through each step to catch calculation mistakes.

Where These Formulas Are Used

Board Exam Problems

Use these formulas for direct numerical questions, proof-based steps, and short-answer reasoning in Mathematics.

Competitive Practice

Memorize the condition of use for each formula so you can identify the right expression quickly under timed practice.

Related Formula Chapters

Coordinate Geometry 1 formulas Geometry 3 formulas Herons Formula 2 formulas Linear Equations In Two Variables 1 formulas Number Systems 4 formulas Polynomials 7 formulas Statistics And Probability 2 formulas Surface Areas And Volumes 2 formulas

These Number Systems formulas help students revise concepts quickly and apply equations accurately in exam-style problems.

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