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Real Numbers

  Mathematics Grade 9 Zambia: Real Numbers Definitions Whole Numbers Whole numbers are positive integers, including 0, without fractions or decimals. They are numbers without any fractional parts. Positive Whole Numbers Positive whole numbers are whole numbers greater than 0. Odd Whole Numbers Odd whole numbers are whole numbers that are not divisible by 2. Even Whole Numbers Even whole numbers are whole numbers that are divisible by 2. Rational Numbers Rational numbers are numbers that can be expressed as the ratio of two integers, i.e., a fraction. Irrational Numbers Irrational numbers are numbers that cannot be expressed as the ratio of two integers, i.e., they have an infinite number of decimal places that never repeat. Real Numbers Real numbers include all rational and irrational numbers. They are numbers that can be found on the number line. Questions and Answers 1. Positive whole numbers less than 20 Start with the number 1. Increment the number by 1 until you reach 20. Writ...
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Laws of Indices and Square Numbers

  Laws of Indices and Square Numbers Laws of Indices Indices are used to show that a number is being multiplied by itself. For example: 2³ means 2 × 2 × 2 3² means 3 × 3 The laws of indices are used to simplify expressions that involve indices. Positive Indices A positive index shows that a number is being multiplied by itself. For example: 2³ = 2 × 2 × 2 = 8 3² = 3 × 3 = 9 Zero Indices Any number with a zero index is equal to 1. For example: 2⁰ = 1 3⁰ = 1 Laws of Indices There are several laws of indices that can be used to simplify expressions: Multiplication Law : aᵐ × aⁿ = aᵐ⁺ⁿ Division Law : aᵐ ÷ aⁿ = aᵐ⁻ⁿ Power Law : (aᵐ)ⁿ = aᵐ×ⁿ Applying the Laws of Indices Using the laws of indices, we can simplify expressions such as: 2³ × 2² = 2³⁺² = 2⁵ 3² ÷ 3¹ = 3²⁻¹ = 3¹ (2²)³ = 2²×³ = 2⁶ Here is the revised text: Laws of Indices Multiplication Law When multiplying powers with the same base, add the exponents. aᵐ × aⁿ = aᵐ⁺ⁿ Examples 2³ × 2⁵ = 2³⁺⁵ = 2⁸ 3² × 3⁴ = 3²⁺⁴ = 3⁶ Division Law ...
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