Identifying the Place Value of a Digit

Every digit in a number tells you two things: what it is (0 through 9) and where it sits. That position, called its place value, decides how much the digit is actually worth. Identifying the place value of a digit is the skill of reading a number and saying exactly what each digit represents, whether it is sitting in the ones place, the tens place, the hundreds place, or further along in a large number.

In our number system, the position of a digit inside a number changes its value. The digit 5 means something very different in 5, in 50, and in 500. That is because each position, moving from right to left, is worth ten times more than the one before it:

• Ones place: the value of the digit by itself
• Tens place: the digit multiplied by 10
• Hundreds place: the digit multiplied by 100
• Thousands place: the digit multiplied by 1,000
• Ten thousands place: the digit multiplied by 10,000
• Hundred thousands place: the digit multiplied by 100,000

This pattern is the foundation for reading a place value table and for later work such as writing a number in expanded form.

A place value chart lines up each digit under a labeled column so you can see its position at a glance. Look at the number 483,927 broken down by place:

Notice that the digit 3 sits in the thousands place, so its value is \(3 \times 1{,}000 = 3{,}000\), not just 3. Practicing with a full place value table makes this pattern easy to apply to any size of number.

To identify the place value of a digit, follow three steps:

1. Count the positions from right to left, starting with ones, then tens, then hundreds, and so on.
2. Find the digit you need and note which column it lands in.
3. Multiply the digit by the value of that column to find its actual value in the number.

For example, in the number 7,246, the digit 2 is in the hundreds place, so its value is \(2 \times 100 = 200\). The digit 7 is in the thousands place, so its value is \(7 \times 1{,}000 = 7{,}000\).

Many practice questions ask you to find the value of the underlined digit inside a larger number. The process is exactly the same, you just start by identifying which place the underlined digit occupies.

Example: In the number 56,381, the digit 6 is underlined. Counting from the right, 6 sits in the thousands place, so its value is \(6 \times 1{,}000 = 6{,}000\).

Example: In the number 904,215, the underlined digit 4 sits in the thousands place as well, since it is the fourth digit from the right, giving a value of \(4 \times 1{,}000 = 4{,}000\).

A common mistake is confusing the digit with its value. The digit is simply the number written down (4, 6, or 9), while the value depends on where that digit sits, for example \(4\) in the thousands place is worth \(4{,}000\), while the same \(4\) in the tens place is only worth \(40\).

Once you can reliably identify the place value of a digit, you are ready to compare numbers, round them, and rewrite them in different forms. These skills connect directly to comparing the values of multi-digit numbers and to converting a number between different place value groupings. Understanding place value is also the base for reading and writing large numbers correctly, since each digit's spoken name depends entirely on its position.

Try identifying the place value of the digit 5 in each number below before checking the answer:

• Number: 3,528 → the digit 5 is in the hundreds place, so its value is \(5 \times 100 = 500\).
• Number: 58,102 → the digit 5 is in the ten thousands place, so its value is \(5 \times 10{,}000 = 50{,}000\).
• Number: 216,459 → the digit 5 is in the tens place, so its value is \(5 \times 10 = 50\).

The digit stays the same in each case, but the value changes completely depending on its place, which is exactly why identifying the place value of a digit is such an important first step before moving on to expanded form and larger place value conversions.

Related lessons

• Math 3