Grade 5
  1. Number Sense and Place Value  1.1. Understanding Large Numbers  1.2. Place Value up to Millions  1.3. Comparing and Ordering Numbers  1.4. Rounding Whole Numbers  1.5. Expanded Form and Standard Form  1.6. Estimation in Calculations
  2. Operations with Whole Numbers  2.1. Addition of Large Numbers  2.2. Subtraction of Large Numbers  2.3. Multiplication Concepts and Strategies  2.4. Division Concepts and Strategies  2.5. Multi-Digit Multiplication  2.6. Long Division  2.7. Order of Operations
  3. Fractions  3.1. Introduction to Fractions  3.2. Equivalent Fractions  3.3. Simplifying Fractions  3.4. Comparing and Ordering Fractions  3.5. Addition and Subtraction of Fractions  3.6. Multiplication of Fractions  3.7. Division of Fractions  3.8. Mixed Numbers and Improper Fractions  3.9. Converting Between Improper Fractions and Mixed Numbers
  4. Decimals  4.1. Understanding Decimals  4.2. Place Value in Decimals  4.3. Comparing and Ordering Decimals  4.4. Rounding Decimals  4.5. Addition and Subtraction of Decimals  4.6. Multiplication of Decimals  4.7. Division of Decimals  4.8. Converting Decimals to Fractions and Vice Versa
  5. Measurement  5.1. Length Measurement (Metric and Customary Units)  5.2. Weight and Mass Measurement  5.3. Volume and Capacity Measurement  5.4. Area of Squares and Rectangles  5.5. Perimeter of Polygons  5.6. Time and Elapsed Time  5.7. Temperature  5.8. Understanding Metric Conversions
  6. Geometry  6.1. Types of Lines and Angles  6.2. Measuring Angles  6.3. Classifying Triangles  6.4. Properties of Quadrilaterals  6.5. Symmetry and Reflection  6.6. Transformations (Translation, Rotation, Reflection)  6.7. Coordinate Plane and Plotting Points  6.8. 3D Shapes and Their Properties  6.9. Nets of 3D Shapes  6.10. Understanding Congruence and Similarity
  7. Data and Probability  7.1. Introduction to Data Collection  7.2. Organizing Data (Tables and Tally Charts)  7.3. Graphs (Bar Graphs, Line Plots, Pictographs)  7.4. Mean, Median, and Mode  7.5. Range of Data  7.6. Introduction to Probability  7.7. Simple Events and Outcomes  7.8. Probability of Independent Events
  8. Ratios and Proportions  8.1. Understanding Ratios  8.2. Writing and Simplifying Ratios  8.3. Equivalent Ratios  8.4. Introduction to Proportions  8.5. Solving Proportion Problems
  9. Algebraic Thinking  9.1. Understanding Variables and Expressions  9.2. Writing Algebraic Expressions  9.3. Simplifying Expressions  9.4. Solving One-Step Equations  9.5. Understanding Patterns and Sequences  9.6. Using the Distributive Property
  10. Financial Literacy  10.1. Introduction to Money and Currency  10.2. Budgeting Basics  10.3. Saving and Spending  10.4. Understanding Interest  10.5. Basic Financial Planning  10.6. Simple vs. Compound Interest

Grade 5 → Decimals ↓


Place Value in Decimals


Numbers are all around us, and they help us in many ways, especially in understanding quantities. Decimals, as numbers, allow us to deal with quantities that are not whole, allowing us to express values that are between whole numbers. For example, when we measure things like weight, height, or even money, we often need to use decimals to be precise. At the core of understanding decimals is the concept of place value. Let's dive deeper into this fascinating concept and understand how place value works with decimals.

What is local value?

Place value refers to the value of a digit based on its position or place in a number. The value of each position in a number is ten times the value of the position to its right. This is called the "base ten" system. It works like this:

    Thousand Hundred Ten One . Tenth Hundredth Thousandth 5 3 2 8 . 4 6 7
    Thousand Hundred Ten One . Tenth Hundredth Thousandth 5 3 2 8 . 4 6 7

In the above number, each digit has a different value according to its position:

  • 5 is in the thousands place, so it represents 5,000.
  • 3 is in the hundreds place, so it represents 300.
  • 2 is in the tenth place, so it represents 20.
  • The 8 is in the one place, so it represents 8.
  • 4 is in the tenths place, so it represents 0.4.
  • The 6 is in the hundredths place, so it represents 0.06.
  • 7 is in the thousandths place, so it represents 0.007.

The decimal point is important because it separates the whole number part from the fractional part.

Decimal point and its role

The decimal point is a point that separates whole numbers from fractional parts. In the number 52.647, the decimal point appears between 52 (the whole number) and 647 (the decimal fraction). When you see a decimal in a number, it tells you that the places beyond the decimal point are fractions of ten.

Visual example:

thousands Hundreds Tens people Tenth Hundred thousandth 5 2 7 1 , 6 4 3

Each column from the decimal point represents a power of ten, going up on the left and down on the right:

Dividing place values in decimals

Let us look more closely at each place value in a decimal number to understand what each one contributes to the overall number.

Whole number place value

  • Units place: It is located just before the decimal point. For the number 13.76, '3' is in the units place.
  • Tens place: It is the second place to the left of the decimal point. In 13.76, '1' is in the tens place which represents ten.

Decimal fraction place value

  • Decimal place: It is the first place just after the decimal point. Here the digit represents the tenths. In 13.76, '7' is in the tenths place which represents 0.7.
  • Hundredths place: The second place after the decimal point. It represents hundredths. In 13.76, '6' is in the hundredths place which represents 0.06.

Understand with more examples

Let us look at some examples to understand this concept better.

Example 1: Understanding 45.89

  • 45 is our whole number portion.
  • The 8 is in the tenths place, and means 8/10, or 0.8.
  • 9 is in the hundredths place, and means 9/100 or 0.09.
  • So, 45.89 gives us four tenths (40), five ones (5), eight-tenths (0.8), and nine-hundredths (0.09).
    45.89 = 40 + 5 + 0.8 + 0.09
    45.89 = 40 + 5 + 0.8 + 0.09

Example 2: Division of 2.345

  • 2 is in the ones place.
  • 3 is in the tenths place, representing 0.3.
  • The 4 is in the hundredths place, representing 0.04.
  • 5 is in the thousandths place, which represents 0.005.
  • When we add this up: 2.345 = 2 + 0.3 + 0.04 + 0.005.
    2.345 = 2 + 0.3 + 0.04 + 0.005
    2.345 = 2 + 0.3 + 0.04 + 0.005

Decimal place values extended beyond thousandths

Sometimes, decimals can extend beyond thousandths, including ten-thousandths, and so on. Let's look at an example of this.

Example 3: Understanding 0.6789

  • 6 is in the tenths place, which represents 0.6.
  • The 7 is in the hundredths place, which represents 0.07.
  • 8 is in the thousandths place, which represents 0.008.
  • 9 is in the ten thousandths place, representing 0.0009.
    0.6789 = 0.6 + 0.07 + 0.008 + 0.0009
    0.6789 = 0.6 + 0.07 + 0.008 + 0.0009

Playing with big numbers and decimals

As we understand the concept of decimal place values, it also helps us work with larger numbers. It is important to continue looking at numbers in terms of their place values as it not only aids understanding but also ensures accuracy in calculations.

Example 4: Breaking down large numbers: 1456.789

  • 1 is in the thousands place which represents 1000.
  • 4 is in the hundreds place which represents 400.
  • 5 is in the tenth place which represents 50.
  • 6 is in a position that represents 6.
  • 7 is in the tenths place which represents 0.7.
  • 8 is in the hundredths place which represents 0.08.
  • 9 is in the thousandths place which represents 0.009.
    1456.789 = 1000 + 400 + 50 + 6 + 0.7 + 0.08 + 0.009
    1456.789 = 1000 + 400 + 50 + 6 + 0.7 + 0.08 + 0.009

The important value of decimal places in life

Understanding decimal place values is helpful in many real-life scenarios. It's not just math - it's used in scientific measurements, financial transactions, cooking, and even when pricing and budgeting.

Example: Money and finance

Think about money. If you have $23.47, it means twenty-three dollars and forty-seven cents. Here, '47' are cents, which are parts of a dollar. Thus, decimal knowledge helps in many everyday activities.

Conclusion: Mastering decimals

Gaining an understanding of place values within decimals is an essential aspect of mathematics at every level of education. It helps develop an intuitive feel for numbers, and it enables us to communicate accurate information about the world around us. With practice, the concept of place value can become a reliable math tool for any situation involving decimals and beyond.

Keep practicing!

The best way to get really good at figuring out place value in decimals is to practice with different problems. Try breaking down the numbers the way we did here and before you know it, you'll be proficient at identifying and using decimal place values!


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Understanding Decimals
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Place Value in Decimals

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