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 → Whole Numbers ↓


Place Value and Face Value


Whole numbers are an essential part of mathematics and understanding their structure is important for mastering many other concepts in mathematics. Two basic ideas to understand when dealing with whole numbers are place value and face value.

Place value

The place value of a digit in a number tells you how much that digit is worth, based on its position. In our number system, called the decimal or base-10 system, the place value of each digit is ten times the digit to its right. This system is based on powers of 10.

The place values from right to left are units, tens, hundreds, thousands, ten thousands, hundred thousands, etc. Let us look at an example to understand this better.

                5 7 8 3
              
              1000s 100s 10s 1s

In the number 5783,

  • The digit 3 is in units place and its place value 3 × 1 = 3.
  • The digit 8 is in the tens place and its place value is 8 × 10 = 80.
  • The digit 7 is in the hundreds place and its place value 7 × 100 = 700.
  • The digit 5 is in the thousandth place and its place value is 5 × 1000 = 5000.

Face value

The face value of a digit is simply the value of that digit, no matter where it is placed in the number. It is the digit that appears in the number.

In the number 5783,

  • The face value of 3 is 3.
  • The face value of 8 is 8.
  • The face value of 7 is 7.
  • The face value of 5 is 5.

Place value vs. face value

To understand the difference between place value and face value clearly, let us consider another example.

                6 2 4 1
              
              1000s 100s 10s 1s

In the number 6241,

  • For issue 4:
    • Face value: 4
    • Place value: 4 × 10 = 40
  • For issue 2:
    • Face value: 2
    • Place value: 2 × 100 = 200
  • For number 6:
    • Face value: 6
    • Place value: 6 × 1000 = 6000
  • For Issue 1:
    • Face value: 1
    • Place value: 1 × 1 = 1

Visualizing place value

Let's visualise the number 3521 to strengthen our understanding of place value.

3 thousand 5 hundred 2 ten 1 one

Expanded form using place value

The concept of place value is also used to write numbers in their expanded form. The expanded form breaks down the number to show the value of each digit.

Let's write the number 4739 in expanded form:

            4739 = 4000 + 700 + 30 + 9

Explanation:

  • 4 is in thousands place, so it represents 4000.
  • 7 is in the hundreds place, so it represents 700.
  • 3 is in the tens place, so it represents 30.
  • 9 is in units place, so it represents 9.

Practice problems

Practice your understanding of place value and face value with these exercises:

  1. Find the place value and face value of digit 6 in the number 6894.
  2. What is the expanded form of number 5281?
  3. Find the local value and face value of all digits of the number 30507.
  4. Write the number 9456 in expanded form.

Answer key

  1. Number: 6894
    • Place value of 6: 6000
    • Face value of 6: 6
  2. Number: 5281 
                    5281 = 5000 + 200 + 80 + 1
  3. Number: 30507
    • Place value of 3: 30000; Face value: 3
    • Place value of 0: 0; Face value: 0
    • Place value of 5: 500; Face value: 5
    • Place value of 0: 0; Face value: 0
    • Place value of 7: 7; Face value: 7
  4. Number: 9456 
                    9456 = 9000 + 400 + 50 + 6

Conclusion

Understanding place value and face value in maths is very important and helps to build a strong foundation for learning complex maths concepts. Place value tells you the value of a digit based on its position in the number, while face value is just the digit itself. Practice these concepts regularly to gain a deeper understanding and improve your number sense.


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Place Value and Face Value

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