📚 Practice With Worksheets
Practice decimal place value, rounding decimals, and identifying equivalent fraction and decimal representations.
▶️ Learn With Videos
Review how place value connects to fractions, decimals, percents, and repeating decimal representations.
🛠️ How to Use This Tool
Use the Place Value Explorer to study digits in whole numbers and decimals. Select any digit to see its place and its value.
The place-value chart shows where each digit belongs, including millions, thousands, hundreds, tens, ones, tenths, hundredths, and thousandths.
Select Show Expanded Form to break the number apart into the value of each nonzero digit.
Select Random Number to generate another whole number or decimal to explore.
🧠 Things to Notice
Moving one place to the left makes a digit’s value ten times greater. Moving one place to the right makes its value one-tenth as great.
A digit can have a very different value depending on its position. In \(52.5\), the first \(5\) represents \(50\), while the second \(5\) represents \(0.5\).
The decimal point separates the whole-number places from the places representing parts of one whole.
📘 Vocabulary
Place Value: The value of a digit based on its position in a number.
Digit: A symbol used to write numbers. The digits are \(0,1,2,3,4,5,6,7,8,\) and \(9\).
Value: What a digit is worth in a number. In \(400\), the digit \(4\) has a value of \(400\).
Whole Number: A number without a fractional or decimal part, such as \(0\), \(7\), or \(384\).
Decimal: A number that uses a decimal point to represent whole numbers, parts of a whole, or both.
Decimal Point: The point that separates the whole-number part from the decimal part.
Tenths: The first place to the right of the decimal point.
Hundredths: The second place to the right of the decimal point.
Expanded Form: A way to write a number as the sum of the values of its digits.
🔢 How to Identify a Digit’s Place and Value
Locate the digit in the number and match its position to the place-value chart. The place tells where the digit is located. The value tells how much the digit is worth in that position.
| Thousands | Hundreds | Tens | Ones | Decimal Point | Tenths | Hundredths | Thousandths |
|---|---|---|---|---|---|---|---|
| 4 | 7 | 2 | 5 | . | 6 | 8 | 3 |
Step 1: Find the Digit
In the number \(4{,}725.683\), locate the digit \(2\). It appears two places to the left of the decimal point.
Step 2: Name the Place
The digit \(2\) is in the tens place.
Step 3: Determine the Value
Because \(2\) is in the tens place, its value is \(2\times10=20\).
Decimal example: In \(4{,}725.683\), the digit \(8\) is in the hundredths place. Its value is \(0.08\).
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