Grade 4
  1. Numbers and Place Value  1.1. Understanding Place Value  1.2. Reading and Writing Large Numbers  1.3. Comparing and Ordering Numbers  1.4. Rounding Numbers  1.5. Understanding Odd and Even Numbers  1.6. Number Patterns and Sequences
  2. Addition and Subtraction  2.1. Addition of Large Numbers  2.2. Subtraction of Large Numbers  2.3. Estimation in Addition and Subtraction  2.4. Word Problems on Addition and Subtraction
  3. Multiplication and Division  3.1. Understanding Multiplication  3.2. Multiplying Multi-Digit Numbers  3.3. Understanding Division  3.4. Dividing Multi-Digit Numbers  3.5. Multiplication and Division Facts  3.6. Word Problems on Multiplication and Division
  4. Factors and Multiples  4.1. Understanding Factors  4.2. Finding Common Factors  4.3. Understanding Multiples  4.4. Finding Common Multiples  4.5. Prime and Composite Numbers  4.6. Prime Factorization  4.7. Greatest Common Factor  4.8. Least Common Multiple
  5. Fractions  5.1. Understanding Fractions  5.2. Equivalent Fractions  5.3. Simplifying Fractions  5.4. Comparing and Ordering Fractions  5.5. Addition of Fractions  5.6. Subtraction of Fractions  5.7. Mixed Numbers and Improper Fractions  5.8. Converting Mixed Numbers to Improper Fractions  5.9. Word Problems on Fractions
  6. Decimals  6.1. Understanding Decimals  6.2. Reading and Writing Decimals  6.3. Comparing and Ordering Decimals  6.4. Rounding Decimals  6.5. Addition of Decimals  6.6. Subtraction of Decimals  6.7. Converting Decimals to Fractions  6.8. Converting Fractions to Decimals  6.9. Word Problems on Decimals
  7. Measurement  7.1. Length  7.1.1. Units of Length  7.1.2. Converting Units of Length  7.1.3. Perimeter  7.1.4. Area  7.1.5. Word Problems on Length  7.2. Weight  7.2.1. Units of Weight  7.2.2. Converting Units of Weight  7.2.3. Word Problems on Weight  7.3. Volume and Capacity  7.3.1. Units of Volume  7.3.2. Converting Units of Volume  7.3.3. Estimating Volume and Capacity  7.3.4. Word Problems on Volume and Capacity  7.4. Time  7.4.1. Reading Time  7.4.2. Units of Time  7.4.3. Converting Units of Time  7.4.4. Calculating Elapsed Time  7.4.5. Word Problems on Time
  8. Geometry  8.1. Properties of Shapes  8.1.1. Types of Angles  8.1.2. Types of Triangles  8.1.4. Symmetry  8.1.5. Lines of Symmetry  8.2. Perimeter and Area  8.2.1. Perimeter of Rectangles  8.2.2. Perimeter of Other Shapes  8.2.3. Area of Rectangles  8.2.4. Area of Other Shapes  8.2.5. Area of Irregular Shapes  8.3. Coordinate Geometry  8.3.1. Understanding Coordinates  8.3.2. Plotting Points on a Grid  8.3.3. Identifying Shapes on a Grid
  9. Data and Graphs  9.1. Types of Data  9.2. Organizing Data  9.3. Reading Bar Graphs  9.4. Drawing Bar Graphs  9.5. Line Plots  9.7. Reading and Interpreting Line Graphs  9.8. Word Problems on Graphs
  10. Money  10.1. Understanding Money  10.2. Addition and Subtraction with Money  10.3. Making Change  10.4. Multiplying and Dividing Money  10.5. Word Problems on Money

Grade 4 ↓


Numbers and Place Value


Welcome to the world of numbers, where each digit has a special place. In this guide, we'll explore the concept of place value, an essential foundation in math that helps us understand the value of numbers based on their location.

What is local value?

Place value indicates the value of a digit depending on where it is located in a number. For example, in the number 234, the digit 2 represents 200, the digit 3 represents 30, and the digit 4 represents 4.

Understanding the value of each space

Let's analyze the number 754 to understand the place value:

  Hundreds | Tens | Units
,
    7 | 5 | 4

- Hundreds place: The digit 7 is in the hundreds place and its value is 700.
- Tens place: The digit 5 is in the tens place and represents 50.
- Units place: The digit 4 is in the units place and is simply 4.

So, when we add these up, we get:

700 + 50 + 4 = 754

Importance of zero in place value

Zero is a special number in place value because it can dramatically change the value of a number depending on its position. For example:

204 vs 240

- The zero in the tens place in 204 indicates that there are no tens in this number. The value of the number is added as follows:

200 + 0 + 4 = 204

- In 240 the zero is in the ones place, which indicates that there is no one:

200 + 40 + 0 = 240

Discovery of big numbers

As numbers get larger, understanding place value becomes even more important. Let's take a look at the number 3,578:

  thousands | hundreds | tens | units
,
    3 | 5 | 7 | 8

- Thousands place: The digit 3 represents 3000.
- Hundreds place: Number 5 represents 500.
- Tens place: The digit 7 represents 70.
- Units place: The digit 8 is 8.

Adding these together gives:

3000 + 500 + 70 + 8 = 3,578

A visual example of place value

3,275 Thousands Hundreds Tens Units

In this visual, each digit of 3,275 is shown pointing to its corresponding place value. This helps us visualize how each digit is part of the whole number.

Common mistakes related to place value

It's easy to make mistakes when dealing with place value, especially when reading numbers containing zeros. For example, consider the number 4005:

  thousands | hundreds | tens | units
,
    4 | 0 | 0 | 5

People often overlook zero, which can lead to misinterpretations, such as thinking there are two hundreds and tens:

4000 + 0 + 0 + 5 = 4005

Here zero means there are no hundreds or tens.

Exercises to improve understanding

Let's practice identifying and adding place values in numbers with the following exercises:

Exercise 1: Divide the number 6,482 into place values.

  thousands | hundreds | tens | units
,
    6 | 4 | 8 | 2

- Solution:

6000 + 400 + 80 + 2 = 6,482

Exercise 2: Which number will be represented by:

  thousands | hundreds | tens | units
,
    2 | 5 | 1 | 7

- Solution:

2000 + 500 + 10 + 7 = 2,517

Extension beyond whole numbers

Place value doesn't just apply to whole numbers; it works with decimals, too! Consider the number 12.45. This extends the place value system to the right of the decimal point:

  tens | units | . | tenths | hundredths
,
  1 | 2 | . | 4 | 5

- Before the decimal point: 12 consists of:

10 + 2 = 12

- .45 after the decimal point represents:

0.4 + 0.05 = 0.45

Therefore, 12.45 adds the two to express numbers beyond the decimal point.

Practical applications of place value

Understanding place value has practical benefits in everyday life. Whether measuring quantities, handling money, or working on math problems, place value helps to effectively understand the size of numbers and digit arrays.

Consider how we count money:

  • The $10 bill represents the tens digit
  • A $1 coin represents units

Conclusion and practice

Place value is a fundamental concept that lays the groundwork for more complex numerical operations and understanding in mathematics. By mastering this system of valuing each digit based on its place, students can develop strong mathematical skills and confidence in handling numbers.

Continue practicing by breaking down large numbers, learning how to use zero correctly, and understanding decimals. This guide serves as a stepping stone toward proficiency as we broaden our understanding of math throughout our academic journey.


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Numbers and Place Value

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