Place Value of Digits in Whole Numbers

Hello, and welcome to the first lesson in your math course. We will begin with whole numbers and place value, the system that lets us read, write, compare, and calculate with numbers of any size. Place value will support everything that follows, especially addition and subtraction.

In this lesson, you will learn to identify both the place of a digit and its value in a whole number. By the end, you should be able to look at a number such as $7,503$ and explain why the 5 means 500 while the 3 means only 3.

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Digits, places, and values

A digit is one symbol used to write a number. Our number system uses only these ten digits:

$$0,1,2,3,4,5,6,7,8,9$$

A whole number may have one digit, like 6, or many digits, like $48,021$.

The important idea is this:

A digit’s place is its position in the number. Its value is what that digit is worth in that position.

For example, look at the digit 5 in three different numbers:

Number	Place of the 5	Value of the 5
5	ones	5
50	tens	50
500	hundreds	500

The digit stays the same, but moving it one place to the left makes its value ten times greater.

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The place-value chart

Always begin at the right-hand end of a whole number. The final digit is in the ones place. Moving left, the place names are:

Millions	Hundred thousands	Ten thousands	Thousands	Hundreds	Tens	Ones
$1,000,000$	$100,000$	$10,000$	$1,000$	$100$	$10$	$1$

Each place is worth ten times as much as the place immediately to its right:

• 10 ones make 1 ten.
• 10 tens make 1 hundred.
• 10 hundreds make 1 thousand.
• 10 thousands make 1 ten thousand.

The names repeat in groups: ones, tens, hundreds; then thousands, ten thousands, hundred thousands; then millions, ten millions, hundred millions.

Let’s use that number carefully:

$$7,503$$

Digit	Place	Value
7	thousands	$7,000$
5	hundreds	$500$
0	tens	$0$
3	ones	$3$

So $7,503$ means 7 thousands, 5 hundreds, 0 tens, and 3 ones.

Its expanded form is:

$$7,503=7\times 1,000+5\times 100+0\times 10+3\times 1$$

which can also be written as:

$$7,503=7,000+500+3$$

Expanded form reveals the value contributed by every digit.

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A reliable method for any whole number

When asked for the place or value of a digit, use this method:

1. Start at the right. Label the last digit ones, then move left: tens, hundreds, thousands, and so on.
2. Locate the digit you are asked about.
3. State its place name.
4. State its value by combining the digit with its place.

Consider:

$$48,216$$

Digit	Place	Value
4	ten thousands	$40,000$
8	thousands	$8,000$
2	hundreds	$200$
1	tens	$10$
6	ones	$6$

Be precise with language:

• The place of 8 is the thousands place.
• The value of 8 is 8,000.
• The place of 1 is the tens place.
• The value of 1 is 10.

A common error is saying “the value of 8 is 8” just because the digit is 8. That is true only if the 8 is in the ones place. In $48,216$, the 8 represents eight groups of one thousand, so its value is $8,000$.

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Why zero matters

Zero can have value zero, but it can still be essential because it holds a place. Compare these whole numbers:

Number	Meaning
$104$	1 hundred, 0 tens, 4 ones
$14$	1 ten, 4 ones

The zero in $104$ shows that there are no tens. Without it, the number would become 14, which is very different.

Now consider:

$$30,406$$

Digit	Place	Value
3	ten thousands	$30,000$
0	thousands	$0$
4	hundreds	$400$
0	tens	$0$
6	ones	$6$

Its expanded form is:

$$30,406=30,000+400+6$$

The zeroes contribute no amount themselves, but they keep the 3 in the ten-thousands place and the 4 in the hundreds place. That is why zero is sometimes called a placeholder.

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Reading larger numbers

Commas help us read large whole numbers. They separate digits into groups of three, called periods:

$$3,582,104$$

Millions period	Thousands period	Ones period
3	582	104

Within the number, each digit still has its own place:

Digit	Place	Value
3	millions	$3,000,000$
5	hundred thousands	$500,000$
8	ten thousands	$80,000$
2	thousands	$2,000$
1	hundreds	$100$
0	tens	$0$
4	ones	$4$

Therefore:

$$3,582,104=3,000,000+500,000+80,000+2,000+100+4$$

A comma is not a digit and does not change the value by itself. It is simply a reading aid. The position of each digit is what determines its value.

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A short accuracy checklist

Before you give an answer about place value, check:

• Did you begin counting places from the right, at ones?
• Did you distinguish place from value?
• Did you include zeroes in the chart when they appear?
• Does your value have the correct number of zeroes?

For instance, in $62,307$:

• 6 is in the ten-thousands place and has value $60,000$.
• 2 is in the thousands place and has value $2,000$.
• 3 is in the hundreds place and has value $300$.
• 0 is in the tens place and has value $0$.
• 7 is in the ones place and has value $7$.

Writing a quick place-value chart is usually safer than trying to count positions mentally, particularly for longer numbers.

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Key takeaways

A whole number is written with digits $0$ through $9$, but a digit’s meaning depends on where it is placed.

• The final digit on the right is in the ones place.
• Moving one place left multiplies the value by 10.
• Place names a position, such as hundreds or thousands.
• Value tells what the digit represents, such as 500 or 7,000.
• Zero is a valuable placeholder: it preserves the positions of the other digits.

Next, you will use this understanding to compare and order whole numbers with the symbols $=$, $<$, and $>$.