Place Value - Elementary Math - Steps, Examples & Questions

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Place value

Here you will learn about place value, including the names and values of the different positions.

Students will first learn about place value as part of their work with numbers and operations in base ten in elementary school.

What is place value?

Place value is the value of each digit within a number.

A number is made up of digits. For example, the number $katex is not defined$ has two digits, $katex is not defined$ and $katex is not defined$ The value of each digit can help us understand the size of the number.

To determine the value of a digit within a number you use a place value chart.

For example, for $katex is not defined$ the $katex is not defined$ is in the tens column and the $katex is not defined$ is in the ones column.

This means that the number $katex is not defined$ is equivalent to $katex is not defined$ tens and $katex is not defined$ ones.

$katex is not defined$ tens is the same as $katex is not defined$ and $katex is not defined$ ones is the same as $katex is not defined$

Adding $katex is not defined$ gives us the number $katex is not defined$

What is place value?

Whole number place value

Here are the digits to the left of the decimal point.

Let’s write the number nine million, four hundred and fifty thousand, three hundred and eighty two in the place value chart:

Notice you use a comma after the millions digit $katex is not defined$ and the thousands digit $katex is not defined$

The comma is used to the left of the decimal point to separate $katex is not defined$ digits at a time.

If the value within a column is $katex is not defined$ you must write a zero for that place value. Here, if you missed the $katex is not defined$ in the thousands position, the number would read $katex is not defined$ which is a different number from the number above.

The place value chart above shows positions up to the millions. However, you can use place value to represent very large numbers.

Place Value	Ordinary Number	Power of $katex is not defined$
Thousands	$katex is not defined$	$katex is not defined$
Millions	$katex is not defined$	$katex is not defined$
Billions	$katex is not defined$	$katex is not defined$
Trillions	$katex is not defined$	$katex is not defined$
Quadrillions	$katex is not defined$	$katex is not defined$
Googol	$katex is not defined$ $katex is not defined$ $katex is not defined$ $katex is not defined$	$katex is not defined$

Decimal place value

Here are the digits to the right of the decimal point.

Let’s write the number two and thirty four thousandths in the place value chart:

There is a period after the ones digit $katex is not defined$ The period tells us that the next part of the number is a decimal or less than $katex is not defined$

If the value within a column is $katex is not defined$ you must write a zero for that place value. Here, if you missed the $katex is not defined$ in the tenths position, the number would read $katex is not defined$ which is a different number from the number above.

The place value chart above shows numbers down to the thousandths. However, you can use place value to represent very small numbers.

Place Value	Ordinary Number	Power of $katex is not defined$
Thousandths	$katex is not defined$	$katex is not defined$
Millionths	$katex is not defined$	$katex is not defined$
Billionths	$katex is not defined$	$katex is not defined$
Trillionths	$katex is not defined$	$katex is not defined$

Common Core State Standards

How does this relate to 2nd grade math, 4th grade math and 5th grade math?

Grade 2 – Numbers and Operations in Base 10 (2.NBT.A.3)
Read and write numbers to $katex is not defined$ using base-ten numerals, number names, and expanded form.

Grade 4 – Numbers and Operations in Base 10 (4.NBT.A.2)
Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form.

Grade 5 – Numbers and Operations in Base 10 (5.NBT.A.3)
Read, write, and compare decimals to thousandths.

How to write the value of a digit in a number

In order to write the value of a digit in a number:

Find the digit within the number.
Use the place value chart to find the position.
Write the value of the digit.

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Place value examples

Example 1: whole number place value

What is the value of the digit $katex is not defined$ in $katex is not defined$

Find the digit within the number.

2Use the place value chart to find the position.

The $katex is not defined$ is in the ones column.

3Write the value of the digit.

The value of the digit $katex is not defined$ in the number $katex is not defined$ is $katex is not defined$ ones, or $katex is not defined$

Example 2: whole number place value

What is the value of the digit $katex is not defined$ in $katex is not defined$

Find the digit within the number.

Show step

Use the place value chart to find the position.

Show step

The $katex is not defined$ is in the hundreds column.

Write the value of the digit.

Show step

The value of the digit $katex is not defined$ in the number $katex is not defined$ is four hundreds, or $katex is not defined$

Example 3: whole number place value

What is the value of the digit $katex is not defined$ in $katex is not defined$

Find the digit within the number.

Show step

Use the place value chart to find the position.

Show step

The $katex is not defined$ is in the ten thousands column.

Write the value of the digit.

Show step

The value of the digit $katex is not defined$ in the number $katex is not defined$ is twenty thousands, or $katex is not defined$

Example 4: decimal place value

What is the value of the digit $katex is not defined$ in $katex is not defined$

Find the digit within the number.

Show step

Use the place value chart to find the position.

Show step

The $katex is not defined$ is in the tenths column.

Write the value of the digit.

Show step

The value of the digit $katex is not defined$ in the number $katex is not defined$ is two tenths, or $katex is not defined$

Example 5: decimal place value

What is the value of the digit $katex is not defined$ in $katex is not defined$

Find the digit within the number.

Show step

Recall the place value of that column.

Show step

The $katex is not defined$ is in the hundredths column.

Write the value of the digit.

Show step

The value of the digit $katex is not defined$ in the number $katex is not defined$ is seven hundredths, or $katex is not defined$

Example 6: decimal place value

What is the value of the digit $katex is not defined$ in $katex is not defined$

Locate the digit within the number.

Show step

Use the place value chart to find the position.

Show step

The $katex is not defined$ is in the thousandths column.

Write the value of the digit.

Show step

The value of the digit $katex is not defined$ in the number $katex is not defined$ is four thousandths, or $katex is not defined$

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Teaching tips for place value

When teaching place value, base ten blocks and other manipulatives can be used to help students visualize place value and see how each position relates to the others.

Place value is based on patterns in our number system, which many students will pick up on. Asking questions like “What do you notice about these numbers?” or “How does the value of a number change if you change the place value of the digits?” can encourage students to think more broadly about the underlying structure of our place value system.

Regularly exposing students to place value ideas helps them develop a deeper understanding of our number system. Instead of just using worksheets, incorporate it into math each day with a place value game. Something as simple as “I am thinking of a number that has more than 4 hundreds, what could it be?” can help students remember and think flexibly about place value.

Reinforce the connection between standard form, expanded form and word form by asking students to provide all three for any given number.

Easy mistakes to make

Thousands or thousandths
Numbers to the right of the decimal point are parts of a whole and so they each end in ths. Numbers to the left of the decimal point are whole numbers and do not end in ths.

Including too many digits
All of the digits after a place value position are sometimes wrongly included.
For example, What is the value of $katex is not defined$ in the number $katex is not defined$

Including a oneths column
The first column to the right of the decimal point is the tenths column – there is no oneths column.
For example, What is the value of the digit $katex is not defined$ in the number $katex is not defined$
$katex is not defined$ Two tenths or $katex is not defined$ Two hundredths, or $katex is not defined$
(Thinking that the first decimal $katex is not defined$ (The first decimal position is tenths
position is oneths and the second $katex is not defined$ and the second is hundredths)
is tenths)

Practice place value questions

katex is not defined

katex is not defined

katex is not defined

Two hundreds

The digit $katex is not defined$ is in the tens column, so the value is $katex is not defined$ tens or $katex is not defined$

katex is not defined

katex is not defined

katex is not defined

One hundred thousand

The digit $katex is not defined$ is in the millions column, so the value is $katex is not defined$ million or $katex is not defined$

katex is not defined

katex is not defined

katex is not defined

Ten thousand

The digit $katex is not defined$ is in the thousands column, so the value is $katex is not defined$ thousands or $katex is not defined$

Seven hundreds

Seven tenths

Seven tens

Seven hundredths

The digit $katex is not defined$ is in the hundredths column, so the value is $katex is not defined$ hundredths or $katex is not defined$

Eight thousandths

Eight tenths

Eight thousands

Eight ones

The digit $katex is not defined$ is in the thousandths column, so the value is $katex is not defined$ thousandths or $katex is not defined$

katex is not defined

katex is not defined

Four thousandths

0.4

The digit $katex is not defined$ is in the ones column, so the value is $katex is not defined$ ones or $katex is not defined$

Place value FAQ

Why is $katex is not defined$ important in place value?

Our number system is called Base Ten, because ten is the value used to create the place value groupings. That is why all of the place value positions (like the tens place or hundreds place) are multiples of $katex is not defined$ This is also why younger students practice skip counting by tens, which ultimately helps them recognize patterns in our number system.

Why is place value important?

Place value helps you understand the size of a number and gives meaning to the digits in each position. An understanding of place value can help you when comparing numbers and ordering numbers and is also essential when operating with numbers.

What decimal place value positions are used in 5th and 6th grade?

Per the Common Core, in fifth grade students work with the tenths place, the hundredths place and the thousandths place. Sixth graders should extend this to smaller positions. It is also important to be mindful of standard expectations, as they may vary from state to state.

The next lessons are

Factors and multiples
Fractions
Fractions operations

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