Place Value Worksheets for Large Numbers

Large numbers place value is the study of how numbers with four, five and six digits are built from places that are each ten times the place to the right. The six PDFs on this page cover expanded form, the value of a digit and word form of numbers up to hundred thousands, and every sheet has an answer key. They follow standard 4.NBT.A.2 of the Common Core standards for grade 4 number and operations in base ten, and the notes below show the places, the periods, and how to read and write the numbers.

Pair these with a place value chart to the millions so every digit has its own column.

About these worksheets

Grade 4 children read and write whole numbers up to 1,000,000 using numerals, number names and expanded form (Common Core 4.NBT.A.2). The key idea is that each place is ten times the place to its right: a 4 in the thousands place is worth ten times a 4 in the hundreds place.

• Expanded form of 4-, 5- and 6-digit numbers.
• Value and place of a digit, from ones to hundred thousands.
• Word form both ways, such as “twelve thousand forty” = 12,040.

Reading large numbers

Commas split a number into groups of three digits. Read each group as a number up to 999, then say the group name: 305,619 is “three hundred five thousand, six hundred nineteen”.

Large numbers place value worksheets: what is in the set

There are 6 large numbers place value worksheets on this page, and every one has an answer key except for any cut-out games. Two sheets are expanded form, two are the value of a digit, and two are word form, with numbers up to hundred thousands.

Large numbers place value: the places and the periods

Large numbers place value is built on one idea: each place is ten times the place to its right. A 1 in the tens place is worth ten, in the hundreds place a hundred, and in the thousands place a thousand. The places are grouped in threes, called periods: the ones period, the thousands period and the millions period. Wikipedia’s article on positional notation explains how the system works. This table shows the seven places up to the millions:

The commas in a large number mark the periods. Read each period as a number from 1 to 999, and then say the period name: 305,619 is “three hundred five thousand, six hundred nineteen”. The place value chart tool shows the places as columns, and the hundreds tens and ones page has the three places of the ones period.

Place value thousands worksheets: four, five and six digits

The place value thousands worksheets use numbers from 1,000 to 999,999. There are 9,000 four-digit numbers, 90,000 five-digit numbers and 900,000 six-digit numbers. This table shows the smallest and the biggest of each, with the biggest in words:

Each time a digit is added, there are ten times as many numbers, since each new place has ten possible digits (and the first has nine, because it cannot be zero). The biggest six-digit number, 999,999, is one less than a million.

Expanded form large numbers: the sum of the values

The expanded form large numbers sheets write a number as the sum of the values of its digits. For 45,302 the values are 40,000, 5,000, 300 and 2, and the zero in the tens place adds nothing. This table shows six numbers in expanded form and in words:

Each number in the table has at least one zero, which is the hard case for children. In 40,008 there are three zeros in a row, and the number is forty thousand eight. In 120,040 the zeros hold the thousands, hundreds and ones places. The standard 4.NBT.A.2 asks for numerals, number names and expanded form.

Place value worksheets grade 4: the value of a digit

The place value worksheets grade 4 ask for the value of a digit, and a number can have the same digit in several places. In 5,555 each 5 is worth a different amount. This table shows four numbers and the value of the digit in each place:

The value of a digit is its face value times its place value. A child who sees this will not confuse the 5 in the thousands place with the 5 in the ones place. A useful check is to add up all the values, which should give the number back.

Value of a digit worksheets: what the sheets ask

The two value of a digit worksheets in this pack give a large number with one digit underlined, and ask children to write the place and the value of that digit. The first sheet uses numbers with four, five and six digits, and the second has sixteen more digits in numbers of four to six digits. Every answer key shows the place and the value, so a child who gets the value wrong can see whether the place was wrong too.

Ten times the place to the right: the key idea

Standard 4.NBT.A.1 asks children to recognize that a digit in one place represents ten times what it represents in the place to its right. The diagram above shows the digit 4 moving from the ones place to the hundred thousands place, and each step is a multiplication by 10. This table compares the same digit in two numbers:

The rule is that moving a digit one place to the left makes it worth ten times as much. This is the basis for multiplying and dividing by 10, and for the decimal places that come in the decimal place value page.

Word form worksheets: reading large numbers

The word form worksheets ask for numbers in words, and words in numbers. The way to read a large number is to read each group of three digits as a number from 1 to 999, and then add the group name. In US schools, “and” is not used in whole numbers. This table shows six numbers, with the word form:

The number 100,000 is “one hundred thousand”, and 7,005 is “seven thousand five”. A zero in a group means nothing is said for that group. The names of large numbers article on Wikipedia has the names for even bigger numbers, such as millions and billions.

Making the biggest and the smallest number

A good activity for large numbers place value is to make the biggest and the smallest number from a set of digit cards. To make the biggest, put the biggest digit in the biggest place. To make the smallest six-digit number, put the smallest digit that is not zero in the first place, and then the zero. This table shows three sets of cards:

The smallest number cannot start with a zero, since 053,619 is just 53,619. The comparing large numbers and rounding large numbers pages use these numbers for comparing and rounding.

Common mistakes with large numbers place value

The most common mistake is to lose a zero. This table shows five mistakes, what went wrong and the fix:

Large numbers place value word problems

Large numbers come up in stadiums, cities and sales. Ask children to underline the digit, to say its place, and then to give its value:

Games and activities for large numbers place value

Children learn large numbers place value best when they play with it. These games use things that are found at home or in a classroom:

• Digit cards: draw six digit cards and make the biggest and the smallest number
• Place value bingo: a bingo card with values, and calling cards with digits in numbers
• Say it right: take turns reading a six-digit number aloud, and check with a partner
• Ten times: say a number, and have a partner say ten times as much
• Value race: roll a die and place it in a six-digit number, trying to make the biggest
• Expanded form match: match numbers with their expanded forms

Extra support and extra challenge with large numbers place value

For children who need more support: use a place value chart with the periods marked, and put the digits in. Always read from the left, and say the group name at each comma. Keep to four-digit numbers first, then five, then six. Write each digit’s value under it, and add them up to check the number. Use the answer key to find where a mistake started.

For children who need more challenge: ask for the number that is 10 times 45,302, for the number that is one less than a million in words, and for all the numbers that can be made with the digits 1, 0 and 5 once each. Writing a story with a number in the hundred thousands is a good challenge.

How to tell that a child is ready to move on from large numbers place value

Before moving on from large numbers place value, check that the child can do all four of these things:

1. The child writes a number of up to six digits in expanded form.
2. The child says the value of any digit.
3. The child reads and writes large numbers in words.
4. The child knows that each place is ten times the place to its right.

When all four are true, move on to the comparing large numbers page, or to the rounding large numbers page.

A 20-minute lesson on large numbers place value

A short lesson is the best way to introduce large numbers place value. This 20-minute plan can be used in a classroom, at a tutoring session or at home, and it uses the worksheets at the end:

Where large numbers place value fits across the grades

No skill stands alone. This table shows what children learn before and after large numbers place value, with the standard that goes with each step:

This page is the main page for large whole numbers. The whole sequence is on the place value worksheets page.

Helping at home with large numbers place value

Parents do not need to be experts to help with large numbers place value. These suggestions work well, and each takes only a few minutes:

• Read large numbers aloud with the child, such as populations in the news.
• Ask for the value of a digit in a price or a distance.
• Make a place value chart and put digit cards in it.
• Play “make the biggest number” with a deck of cards.
• Check answers with the answer key, and ask the child to explain one.

How to check progress in large numbers place value

A teacher or parent can check progress in large numbers place value with the answer key and a few questions. This table shows three common situations, what they mean and what to do next:

A five-day plan for large numbers place value

Most children need about a week of short sessions for large numbers place value. This plan follows the order of the worksheets on this page:

When the plan for large numbers place value is complete, move on to the comparing large numbers page. The whole sequence is on the place value worksheets page.