Place Value Worksheets

TABLE OF CONTENTS

• What Is Place Value and Why It Matters
• How Place Value Works
• Place Value Whole Number Example
• Place Value with Decimals
• Common Place Value Misconceptions and Sudent Mistakes
• Visual Models for Teaching Place Value
• Teaching Place Value by Grade Level
• Printable Place Value Worksheets & Activities
• Interactive Online Place Value Practice
• Place Value Practice Problems
• Frequently Asked Questions About Place Value
• Place Value Term Glossary
• Place Value Summary: Standards Alignment & Author Credentials

What Is Place Value and Why It Matters

Place value is the system we use to determine the value of each digit in a number based on its position. For example, in the number 432, the 3 is in the tens place, so it represents 30. This concept is often taught using a place value chart to help elementary students visualize how numbers are built.
In 5,428 the digit "4" represents 400 (i.e. 4 hundreds).

Place value is the value a digit has based on its position in a number. Place value helps us read, write, compare, and understand numbers of all sizes. Below you'll find clear explanations, examples, and printable worksheets for grades K–8.

Understanding place value is essential because it helps students:

• Build strong number sense
• Read and write large numbers
• Compare and order numbers correctly
• Add and subtract using regrouping
• Understand decimals and fractions
• Break apart numbers using expanded form and word form
• Add and subtract multi-digit numbers correctly

How Place Value Works

1. Write the number and label each digit's place (e.g. thousands, hundreds, tens, ones).
2. Multiply each digit by the value of its place.
3. Add up those values to get the number in standard form (though this is just restating the number).

Place Value Whole Number Example

Whole numbers include zero and all positive integers. As numbers get larger, the place value of each digit added to the left is 10 times greater than the place value of the digit to its right. This also means that the place value of each digit to the right is 10 times smaller than (or 1/10 the size of) the digit to its left.

Millions | Hundred Thousands | Ten Thousands | Thousands | Hundreds | Tens | Ones

5 Digits / Ten Thousands Place Value Example

Consider the number 12,345:

• The 1 is in the ten thousands place.
1 × 10,000 = 10,000
• The 2 is in the thousands place.
2 × 1,000 = 2,000
• The 3 is in the hundreds place.
3 × 100 = 300
• The 4 is in the tens place.
4 × 10 = 40
• The 5 is in the ones place.
5 × 1 = 5

Written in expanded form: 10,000 + 2,000 + 300 + 40 + 5

Place Value With Decimals

Decimals represent fractions of a whole. A decimal point is inserted to the right of the ones place. As with whole number place values, each digit’s value is 10 times smaller than (or 1/10 the size of) the digit to its left and 10 times greater than the digit to its right.

Ones | Tenths | Hundredths | Thousandths

• The tenths place represents 1/10
• The hundredths place represents 1/100
• The thousandths place represents 1/1000

3 Decimal Points / Thousandths Place Value Example

Consider the number 1.234:

• The 1 is in the ones place.
1 × 1 = 1
• The 2 is in the tenths place.
2 × 1/10 = 2/10 or 0.2
• The 3 is in the hundredths place.
3 × 1/100 = 3/100 or 0.03
• The 4 is in the thousandths place.
4 × 1/1,000 = 4/1,000 or 0.004
• Written in expanded form:
1 + 2/10 + 2/100 + 4/1,000 or 1 + 0.2 + 0.03 + 0.004

Common Place Value Misconceptions & Mistakes Students Make

Here are a few misunderstandings and potential pitfalls students often fall into with place value:

• confusing the digit with the value of the digit, i.e. forgetting that digits must be multiplied by their place value (e.g. in the number 456, thinking the digit 4 represents the value 4 rather than 4 × 100, or 400)
• forgetting that zero is a placeholder (e.g. interpreting the number 507 as 57, forgetting that the 0 represents 0 tens)
• writing digits left to right without recognizing place value (e.g. hearing the number 507 orally and recording it as 5,007 because the number 500 contains two zeroes)
• misaligning place value during addition and subtraction (e.g. aligning whole numbers on the left with different place values rather than on the right by the ones place)
• confusing the relative values of decimal places (e.g. mistakenly believing hundredths are larger than tenths since 100 is greater than 10, therefore thinking the number 0.02 is greater than 0.2)
• believing additional zeroes to the right impact decimal values (e.g. thinking 0.600 is greater than 0.6 because it has more digits)
• mixing up expanded notation with expanded form (expanded notation goes a step further than expanded form by showing the digit and place values as factors in parentheses, e.g. the number 456 in expanded notation is (4 × 100) + (5 × 10) + (6 × 1) and in expanded form is 400 + 50 + 6)

To help students avoid mistakes and confusion, it is important to use visual models such as base-10 blocks or place value charts. It also helps to have students verbalize the value of each digit as they write numbers to reinforce the concept and prevent skipping placeholder zeroes.

Visual Models for Teaching Place Value

Base-Ten Blocks
These blocks help students see and touch place value. They're excellent for teaching regrouping (carrying/borrowing) and engaging tactile learners.

• small cubes = ones
• rods = tens
• flats = hundreds
• large cubes = thousands

Place Value Disks
Place value disks or chips are color-coded circles labeled by place (ones, tens, hundreds, etc.). As an alternative to base-10 blocks, they're great for:

• comparing numbers
• building multi-digit numbers
• demonstrating regrouping

Place Value Charts
Place value anchor charts are important references while students learn place value concepts. However, there are also many blank place value chart activities students can do to reinforce their understanding, including:

• build numbers from verbal descriptions
• compare large or decimal numbers
• convert numbers to expanded form
• slide digits left or right to multiply/divide by 10

Teaching Place Value by Grade Level

Place value concepts are essential to math instruction. Certain place values and place value skills are explicitly taught in early grades and later built upon.

• tens and ones
• counting by tens
• comparing 1- and 2-digit numbers
• properly aligning numbers to add and subtract (within 100)
• beginning number sense

• hundreds and thousands
• counting by fives, tens, and hundreds
• comparing multi-digit numbers
• properly aligning numbers to add and subtract (within 1,000)
• rounding to the nearest ten or hundred
• standard, word, and expanded form

• place value up to millions
• decimal place value (tenths, hundredths, thousandths))
• comparing decimals
• rounding to decimals and all other place values
• properly aligning multi-digit numbers to multiply and divide, including decimals
• multiplying and dividing by powers of 10
• using exponents to denote powers of 10

Although place value is not taught directly in upper grades, core place value concepts are still implicitly used in more advanced math skills such as comparing rational numbers.

Place Value Practice Problems

Identify a digit's value

What is the value of the underlined digit?  48,902

Answer: 6,000
Explanation: Since there is no decimal, we can begin identifying place values starting with the 2 as the ones place and working our way left. The digit 8 is in the thousands place. So, multiply 8 × 1,000 to get the total value of the digit: 8,000)

Recognize place values

Which digit is in the ones place?  23.16

Answer: 3
Explanation: Decimal points always appear to the right of the ones place. The decimal point in this number appears to the right of the digit 3, therefore we know the digit 3 is in the ones place.

Write a number in a different form

Write the number 11,075 in expanded form.

Answer: 10,000 + 1,000 + 70 + 5
Explanation: Expanded form expresses numbers as a sum of their digits’ values. Since there is no decimal point, we know that the digit 5 is in the ones place. The other digits’ place values increase while moving left. Multiply the digits by their respective place values (1 × 10,000, 1 × 1,000, 0 × 100, 7 × 10, and 5 × 1), then express the products as a sum. Note: the hundreds place becomes a placeholder 0 and adds no additional information, so it can be dropped from the final sum.

Write a number in a different form

Write the number fifty-six and three hundredths in standard form.

Answer: 56.03
Explanation: Standard form is the most common form, expressing numbers using numerals. Fifty-six is expressed as 56. The word and in written form indicates a decimal. The place value hundredths indicates the fractional part is out of 100 and goes to the second place value past the decimal point, expressed as 0.03. Combine the components to arrive at the final standard form: 56.03

Order sets of numbers

Order the numbers from least to greatest.  9.651 | 9.564 | 9.609 | 9.059

Answer: 9.059 | 9.564 | 9.609 | 9.651
Explanation: When comparing numbers, begin by identifying the largest digit in the greatest place value in your set. Since the numbers in this set all share a 9 in the ones place, we must move right to the next greatest place value, the tenths place. Here the digits are different: 9.059 has a 0, indicating it is our least value; 9.564 has a 5, indicating it is greater than 9.059, but less than the remaining two numbers, which both have a 6 in the tenths place. For those remaining two numbers, we must move to the next place value again: the hundredths place. The 0 in 9.609 is less than the 5 in 9.651, so we know it is the next in the sequence. That leaves 9.651 as the greatest number.

Place Value Term Glossary

The following are some common terms and concepts related to place value that all students should understand.

• digit - a single numeral (0–9) used to make numbers
• value of a digit - the total worth of a digit based on its position
• ones place - the position showing how many groups of one are in a number
• tens place - the position showing how many groups of ten are in a number
• hundreds place - the position showing how many groups of one hundred are in a number
• thousands place - the position showing how many groups of one thousand are in a number
• ten thousands / hundred thousands / millions place - larger place value positions showing how many groups of their respective values are in a number
• tenths / hundredths / thousandths – the decimal place values representing groups of fractional parts (1/10, 1/100, 1/1000)
• decimal point - the dot separating whole numbers from fractional parts, positioned to the right of the ones place
• expanded form - a number written as the sum of each digit’s value (e.g., 300 + 40 + 5)
• expanded notation - a number written as the sum of the products of each digit and its place value (e.g., (3 × 100) + (4 × 10) + (5 × 1))
• standard form - the most common way to write a number (e.g., 345).
• word form - writing a number in words (e.g., three hundred forty-five).
• base-ten system - our number system, which is based on groups of ten
• comparing numbers - looking at the place value of digits to determine whether numbers are greater than, less than, or equal to one other
• regrouping - rearranging numbers between different place values when adding or subtracting (also called borrowing or carrying)
• rounding - simplifying a number into a more convenient value, always done to a specified place value (e.g. 492 rounded to the nearest 10 is 490, but rounded to the nearest 100 is 500)

Place Value Summary

Place value is about understanding how a digit's position gives it a specific value (ones, tens, hundreds, etc.). By combining clear explanations, worked examples, and downloadable worksheets, this page aims to support teachers, parents, and students. Use the links above to find level-appropriate practice and deepen understanding step by step. These place value learning materials have been created by elementary teachers and accredited educators and aligned to current curriculum / Common Core math standards.