Page 2: Decimal Number Properties and Approximations

This page delves into decimal number properties and introduces the concept of absolute error in approximations.

Definition: Absolute error is the absolute difference between the real value and the approximated value.

Example: For the approximation of 3.46 to 3.5, the absolute error is |3.46 - 3.5| = 0.04

Highlight: The page introduces a number line representation of decimals to visualize their relative positions.

Page 3: Rounding Decimal Numbers

This page focuses on rounding decimal numbers to different decimal places and calculating error bounds.

Example: Rounding 6.82 to different decimal places:

• To units: 7
• To tenths: 6.8
• To hundredths: 6.82
• To thousandths: 6.820

Definition: A rounding error is the difference between the exact value and its rounded approximation.

Page 4: Decimal Operations

This page covers arithmetic operations with decimal numbers, including addition, subtraction, multiplication, and division.

Example: Complex decimal calculations like 2.37 - 1.26 + 0.8 - 0.35 = 1.56

Highlight: The page emphasizes proper alignment of decimal points when performing calculations.

Page 5: Practical Applications

This page applies decimal calculations to real-world scenarios involving money and measurements.

Example: Calculating the cost of 1.083 kg of salmon at 9.75 €/kg = 10.56 €

Highlight: The importance of rounding in practical contexts, especially with monetary calculations.

Page 6: Complex Problem Solving

This page presents complex word problems involving decimal calculations in business and real-estate contexts.

Example: Calculating profit from land sale: Purchase price + urbanization costs - selling price = total profit

Highlight: The importance of systematic problem-solving approaches in multi-step decimal calculations.

Advanced Applications

This section covers more complex real-world applications involving decimal calculations.

Example: Real estate calculation involving a rectangular plot measuring 125.40 m by 74.60 m

Highlight: Complex problems often involve multiple steps and operations with decimals.

Fractions and Decimals

This page explores the relationship between fractions and decimals through practical examples.

Example: Converting fractions to decimals and comparing quantities, such as 13/15 versus 17/20

Definition: The square root algorithm is introduced for precise decimal calculations.

Page 1: Introduction to Decimal Numbers

This page introduces the fundamental concepts of decimal numbers and their classifications. The content focuses on different types of decimal numbers and their ordering.

Definition: Decimal numbers can be classified into exact decimals (like 0.5, 2.5) and inexact decimals.

Example: Periodic pure decimals like 2.333... (written as 2.3̅) and mixed periodic decimals like 2.5333... (written as 2.53̅)

Highlight: Between any two decimal numbers, there are infinitely many other decimal numbers.

Vocabulary: Rational numbers (Q) include both exact and periodic decimals, while irrational numbers (I) are non-periodic decimals like π and √2.