Grade 6
  1. Number System  1.1. Whole Numbers  1.1.1. Place Value and Face Value  1.1.2. Comparing and Ordering Numbers  1.1.3. Rounding Numbers  1.1.4. Properties of Whole Numbers (Associative, Commutative, Distributive)  1.2. Integers  1.2.1. Introduction to Integers  1.2.2. Addition and Subtraction of Integers  1.2.3. Multiplication and Division of Integers  1.2.4. Properties of Integer Operations  1.3. Fractions  1.3.1. Types of Fractions  1.3.2. Equivalent Fractions  1.3.3. Simplification of Fractions  1.3.4. Addition and Subtraction of Fractions  1.3.5. Multiplication and Division of Fractions  1.3.6. Comparing and Ordering Fractions  1.4. Decimals  1.4.1. Understanding Decimals  1.4.2. Conversion between Fractions and Decimals  1.4.3. Addition and Subtraction of Decimals  1.4.4. Multiplication and Division of Decimals  1.4.5. Comparing and Ordering Decimals
  2. Algebra  2.1. Basics of Algebra  2.1.1. Variables and Constants  2.1.2. Expressions and Equations  2.1.3. Algebraic Terms and Coefficients  2.2. Solving Simple Equations  2.2.1. Balancing Equations  2.2.2. Solving One-Step Equations  2.2.3. Solving Two-Step Equations  2.3. Patterns and Sequences  2.3.1. Identifying Patterns  2.3.2. Arithmetic Sequences
  3. Ratio and Proportion  3.1. Ratios  3.1.1. Understanding Ratios  3.1.2. Equivalent Ratios  3.1.3. Simplifying Ratios  3.2. Proportion  3.2.1. Introduction to Proportion  3.2.2. Direct and Inverse Proportions  3.3. Percentages  3.3.1. Converting Ratios to Percentages  3.3.2. Percentage Increase and Decrease  3.3.3. Discount and Profit Calculations  3.3.4. Simple Interest Calculations in Percentages in Ratio and Proportion
  4. Geometry  4.1. Basic Geometric Shapes  4.1.1. Points, Lines, and Angles  4.1.2. Types of Angles  4.1.3. Intersecting and Parallel Lines  4.2. Triangles  4.2.1. Types of Triangles  4.2.2. Properties of Triangles  4.2.3. Sum of Angles in a Triangle  4.2.4. Congruence of Triangles  4.3. Quadrilaterals  4.3.1. Types of Quadrilaterals  4.3.2. Properties of Quadrilaterals  4.4. Circles  4.4.1. Radius and Diameter  4.4.2. Circumference and Area  4.4.3. Arcs and Chords  4.4.4. Sector and Segment
  5. Mensuration  5.1. Perimeter  5.1.1. Perimeter of Simple Shapes  5.2. Area  5.2.1. Area of Rectangles and Squares  5.2.2. Area of Triangles and Parallelograms  5.2.3. Area of Composite Figures  5.2.4. Area of Trapezium  5.3. Volume  5.3.1. Volume of Cubes and Cuboids  5.3.2. Volume of Cylinders  5.3.3. Volume of Cones  5.3.4. Surface Area of Simple Solids
  6. Data Handling  6.1. Introduction to Data  6.1.1. Types of Data  6.1.2. Organizing Data  6.1.3. Frequency Distribution  6.2. Graphs and Charts  6.2.1. Bar Graphs  6.2.2. Line Graphs  6.2.3. Pictographs  6.2.4. Pie Charts  6.3. Mean, Median, and Mode  6.3.1. Calculating Mean  6.3.2. Finding Median  6.3.3. Identifying Mode  6.3.4. Range of Data in Mean, Median, and Mode
  7. Probability  7.1. Basics of Probability  7.1.1. Understanding Probability  7.1.2. Probability of Simple Events  7.1.3. Experimental and Theoretical Probability
  8. Practical Geometry  8.1. Construction of Shapes  8.1.1. Constructing Triangles  8.1.2. Constructing Quadrilaterals  8.1.3. Constructing Circles and Arcs  8.2. Symmetry  8.2.1. Line of Symmetry  8.2.2. Rotational Symmetry  8.2.3. Translational Symmetry

Grade 6 → Number System → Decimals ↓


Conversion between Fractions and Decimals


In math, it's essential to understand the concept of fractions and decimals. Fractions and decimals are two different ways of representing numbers that aren't whole. In this explanation, we'll explore how to convert between fractions and decimals, why it's useful, and how we can use these conversions in real-world scenarios.

What is fraction?

A fraction represents a part of a whole. It has a numerator and a denominator. The numerator is the top number and it shows how many parts we have. The denominator is the bottom number and it tells us how many parts there are in a whole.

Numerator ------ Denominator
Numerator ------ Denominator

For example, the fraction 1/2 tells us that we have 1 part of 2 equal parts of a whole.

Visual example of fractions

Consider the following fraction:

3/4

This means that 3 out of 4 parts are chosen or considered. We can depict this division of the circle as follows:

What is a decimal?

Decimals are another way of representing fractions. In decimals, the whole is divided into ten equal parts, hundred equal parts, thousand equal parts, etc. The numbers are represented by a point called the decimal point.

For example, 0.5 is a decimal number that is equivalent to the fraction 1/2.

Visual example of decimals

The decimal point 0.75 can be viewed as follows:

The shaded portion represents the decimal point 0.75, which represents 75 out of 100.

Converting fractions to decimals

To convert a fraction to a decimal you divide the numerator (the top number) by the denominator (the bottom number).

Step-by-step conversion

Let's convert the fraction 1/4 to decimal:

  • Step 1: Identify the numerator and denominator. Here, numerator = 1, denominator = 4.
  • Step 2: Divide the numerator by the denominator using the long division method.
0.25 __________ 4 | 1.00 - 0 ------ 10 - 8 ------ 20 - 20 ------ 0
0.25 __________ 4 | 1.00 - 0 ------ 10 - 8 ------ 20 - 20 ------ 0

The decimal place of 1/4 is 0.25.

Example: Converting a fraction to another fraction

Let's convert 3/8 to decimal form:

0.375 ___________ 8 | 3.000 - 0 ------- 30 - 24 ------ 60 - 56 ------ 40 - 40 ------ 0
0.375 ___________ 8 | 3.000 - 0 ------- 30 - 24 ------ 60 - 56 ------ 40 - 40 ------ 0

The decimal equivalent of 3/8 is 0.375.

Converting decimals to fractions

To convert a decimal to a fraction, follow these steps:

  • Step 1: Write the decimal divided by 1. This means take the decimal and express it by 1.
  • Step 2: Multiply both the numerator and denominator by 10 until the decimal point disappears.
  • Step 3: Simplify the fraction, if possible.

Step-by-step conversion

Convert 0.75 to a fraction:

  • Step 1: Write the decimal above the 1.
    0.75 / 1
  • Step 2: Multiply both the numerator and denominator by 100 to remove the decimal point.
    0.75 × 100 / 1 × 100 = 75 / 100
  • Step 3: Simplify the fraction.
    75 / 100 = 3 / 4 (dividing both numerator and denominator by 25)

Therefore, 0.75 as a fraction is 3/4.

Example: Another decimal conversion

Convert 0.5 to a fraction:

  • Step 1: Express 0.5 by 1.
    0.5 / 1
  • Step 2: Multiply both the numerator and denominator by 10 to remove the decimals.
    0.5 × 10 / 1 × 10 = 5 / 10
  • Step 3: Simplify the fraction.
    5 / 10 = 1 / 2 (dividing both by 5)

Thus, 0.5 as a fraction is 1/2.

Why is conversion important?

Converting between fractions and decimals is useful in everyday life. Here are some cases:

  1. Money: We most often use decimals to represent money because amounts like $4.25 are easier to understand than fractions.
  2. Measurement: Fractions and decimals are both used in different forms of measurement. For example, recipes may call for 1/2 cup of sugar or an event may start 1.5 hours after noon.
  3. Simplification: Converting fractions to decimals can simplify complex calculations.

Practice problems

Convert fractions to decimals:

  1. Convert 2/5 to decimal.
  2. Convert 7/8 to decimal.
  3. Convert 5/6 to decimal.

Convert decimal to fraction:

  1. Convert 0.25 to a fraction.
  2. Convert 0.125 to a fraction.
  3. Convert 0.6 to a fraction.

Conclusion

Understanding how to convert between fractions and decimals is an important math skill. It helps to compare, simplify, and accurately represent parts of a whole in a variety of mathematical contexts. Through practice and real-life application, the concepts of fractions and decimals become less abstract and more tangible for students, making math more accessible and understandable.


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Conversion between Fractions and Decimals

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