Decimal Place Value

A decimal number is a number that consists of a whole number part and a fractional part, separated by a symbol called the decimal point. The value of each digit in a number depends on its position, which is called the decimal place value. When looking at the digits to the left of the decimal point, we follow the standard whole number structure, counting them as ones, tens, hundreds, and thousands.

Think of everything to the right of the point as parts of a whole. These are the decimal places, representing values smaller than one. The names follow a pattern based on their distance from the decimal point: first come tenths, followed by hundredths, then thousandths. A great way to master this is to use a chart of decimal place values. It gives you a clear visual map, ensuring that whenever you work with decimals, you can instantly identify the value of any digit.

Example:
 

Let's look at the decimal number 45.678:

• 4 is in the Tens place (Value: 40)
• 5 is in the Ones place (Value: 5)
• ( . ) is the Decimal Point
• 6 is in the Tenths place (Value: 0.6)
• 7 is in the Hundredths place (Value: 0.07)
• 8 is in the Thousandths place (Value: 0.008)

Finding the place value of a digit in a decimal number relies entirely on its position relative to the decimal point. The decimal point acts as a separator between the whole number part (left) and the fractional part (right).

Step-by-Step Method
 

1. Identify the Decimal Point: Start here. This dot separates the integers from the decimals.

2. Move to the Left (Whole Numbers): The values increase by multiples of 10.
   • 1st digit to the left: Ones
   • 2nd digit to the left: Tens
   • 3rd digit to the left: Hundreds

3. Move to the Right (Decimal Fractions): The values decrease by multiples of 10. Notice the "-ths" suffix.
   • 1st digit to the right: Tenths (\(\frac{1}{10}\))
   • 2nd digit to the right: Hundredths (\(\frac{1}{100}\))
   • 3rd digit to the right: Thousandths (\(\frac{1}{1000}\))

Example: 29.357
 

To find the place value of each digit in 29.357:
 

• 2 is the second digit to the left \(\rightarrow\) Tens
• 9 is the first digit to the left \(\rightarrow\) Ones
• ( . ) is the Decimal Point
• 3 is the first digit to the right \(\rightarrow\) Tenths
• 5 is the second digit to the right \(\rightarrow\) Hundredths
• 7 is the third digit to the right \(\rightarrow\) Thousandths

A decimal place value chart is a graphical tool or table that helps determine the value of each digit in a number based on its position. It is particularly useful for understanding the place value of decimals, as it visually separates the whole number part (integers) from the fractional part using a decimal point.

• To the Left: The value of the digits increases (Ones, Tens, Hundreds).
• To the Right: The value of the digits decreases (Tenths, Hundredths, Thousandths).

This organization, in a place value chart, helps students and learners easily compare numbers, ensuring they understand that 0.1 (one-tenth) is larger than 0.01 (one-hundredth).

Decimals represent specific values with exactness using place values and support comparisons and calculations to be completed without error. Here are some strategies to support mastering decimal place values:  
 

• Use Money as the Primary Analogy: Since most students are already familiar with coins, use currency to explain decimals. Explain that a dollar represents a "whole" (1.00), a dime represents a "tenth" (0.10), and a penny represents a "hundredth" (0.01). This real-world connection makes the abstract concept of values getting smaller to the right of the decimal point immediately relatable.
   
• Create a "Place Value Slider": Construct a simple paper tool in which a strip of numbers slides through a frame with a fixed decimal point. By moving the number strip left or right, students can visually see how the value of a single digit changes from tens to ones to tenths. This dynamic movement reinforces that position dictates value.
   
• Focus on the "Ones" as the Center: A common misconception is that the decimal point is the center of the number system. Instead, teach students to look at the "Ones" place as the mirror line. Show them how "Tens" and "Tenths" mirror each other, and "Hundreds" and "Hundredths" do the same, radiating out from the ones place.
   
• Utilize Visual Grids: Use 10x10 grids to represent a whole unit. Coloring in one column (10 squares) represents 0.1, while coloring in a single small square represents 0.01. This visual representation helps students physically see the difference in size between a tenth and a hundredth, preventing the error of thinking 0.01 is larger because "hundred" sounds big.
   
• Practice with Expanded Notation: Encourage students to break numbers down into addition problems (e.g., 3.45 = 3 + 0.4 + 0.05). Writing numbers in this expanded form forces them to isolate and identify the value of each specific digit, reinforcing the structure of the number rather than just reading it as a string of digits.
   
• Incorporate Decimals Place Value Worksheets: Consistent, structured practice is essential for retention. Use targeted decimal place-value worksheets that ask students to identify the value of underlined digits or to convert fractions to decimals. These resources provide the repetition needed to build muscle memory for quickly identifying positions like thousandths or ten-thousandths.
   
• Gamify with Number Cards: Give students a set of digit cards and a "decimal point" button. Call out a specific value (e.g., "Make a number with 5 in the hundredths place") and have them race to arrange their cards correctly. This active engagement keeps energy levels high while testing immediate recall of place-value positions.

Decimals express values with accuracy in the number system. Understanding decimal place values helps us compare values more precisely. Given below are a few real-life applications of decimal place value:
 

• Decimal place values help in calculating discounts and taxes accurately. For example, if an item is purchased for $30.82, 8 is in the tenths place and 2 is in the hundredths place.
   
• Engineers ensure the measurements of materials are accurate by checking the decimal place values.
   
• Decimal place values are utilized in calculating the precise time in seconds or milliseconds. For example, 8.48 seconds indicates 8 whole seconds and 48 hundredths of a second.
   
• A vehicle’s mileage is often measured in decimals, such as 18.6 km per liter.
   
• In sports timing, decimals are used to record highly precise measurements, such as a sprinter’s finish time recorded as 9.58 seconds, allowing differentiation down to hundredths or thousandths of a second.