2nd Grade · 4th Grade · 2.NBT.A.3 · 4.NBT.A.2

Expanded form in 2nd and 4th grade

Expanded form writes a number as the sum of what each digit is worth, so 495 becomes $400 + 90 + 5$ . In 2nd grade, your child reads and writes numbers up to 1000 in digits, in words and in expanded form. In 4th grade, your child does the same with numbers up to 1,000,000 and compares two big numbers using >, = and <.

What the standards say

The official Common Core wording, quoted exactly. The plain version follows.

2.NBT.A.3 Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.

4.NBT.A.2 Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

What it means, in plain words

2nd grade: three ways to write a number up to 1000 2.NBT.A.3

A number can be written three ways. Standard form is the usual way with digits: 495. Number names spell the number in words: four hundred ninety-five. Some worksheets call this the word form of numbers. Expanded form adds up the value of each digit: $400 + 90 + 5$ .

Expanded form in 2nd grade makes place value easy to see. Each part of the sum matches one place: 400 is the hundreds, 90 is the tens and 5 is the ones. When a place holds a zero, that part is 0 or is left out, so 406 is $400 + 6$ , or $400 + 0 + 6$ .

Number names have their own traps. Teen numbers and tens sound alike, so fourteen and forty are easy to mix up. Children also learn to put a hyphen in names like ninety-five.

Your child should be able to:

Read and write numbers up to 1000 in digits and in words
Write a three-digit number in expanded form, such as $259 = 200 + 50 + 9$
Turn expanded form back into a number, even when the parts are out of order
Write a number with a zero in it, such as 406, in all three forms

Example

What number is $5 + 80 + 300$ ?

Sort the parts by place: 300 is the hundreds, 80 is the tens and 5 is the ones.
That is 3 hundreds, 8 tens and 5 ones.
$300 + 80 + 5 = 385$ , so the number is 385, three hundred eighty-five.

4th grade: bigger numbers, and comparing them 4.NBT.A.2

Expanded form in 4th grade works the same way with more places: thousands, ten thousands and hundred thousands. The number 62,814 in expanded form is $60{,}000 + 2{,}000 + 800 + 10 + 4$ .

Number names get longer too. The comma splits a big number into groups of three digits. Your child reads the group before the comma like a smaller number and adds the word thousand, then reads the last three digits. So 62,814 is sixty-two thousand, eight hundred fourteen.

4th graders also compare two numbers and write the result with > (greater than), < (less than) or = (equal to). Your child lines up the two numbers by place, ones under ones. If one number reaches a higher place, such as ten thousands, it is greater. Otherwise your child compares from the left, and the first place where the digits differ decides.

Your child should be able to:

Write numbers in the thousands in standard form, as number names and in expanded form
Read a big number by its comma groups, such as forty-one thousand, two hundred six for 41,206
Compare two big numbers by lining up their places, and write the result with >, = or <
Explain which place decides a comparison

Example

Which is greater, 57,309 or 57,390? Write the comparison with > or <.

Line up the places. Both numbers have 5 ten thousands and 7 thousands.
Both have 3 hundreds.
In the tens place, 57,309 has 0 tens and 57,390 has 9 tens.
9 tens is more than 0 tens, so 57,390 is greater: $57{,}309 < 57{,}390$ .

Where children usually get stuck

Your child writes 539 in expanded form as $5 + 3 + 9$ .
The child splits the number into its digits and forgets that each digit is worth its place. The 5 stands for 5 hundreds, so the first part is 500.
What helps. Write 500, 30 and 9 on strips of paper, each strip as long as its number. Stack them with the right edges lined up and the longest at the bottom. The top digits now read 539.
Your child writes three hundred six as 3006.
The child writes each part as it is heard: 300, then 6. The words name the parts of the number, but in digits the parts share places, so the 6 goes into the ones place of 300.
What helps. Draw three boxes for hundreds, tens and ones. Say the number name slowly and put one digit in each box, with a 0 in any empty box: 306.
Your child writes $34{,}582 > 34{,}628$ because 8 is bigger than any digit in 34,628.
The child looks for the biggest digit anywhere in the number. Only the first place from the left where the digits differ decides, and here that is the hundreds: 5 hundreds is less than 6 hundreds.
What helps. Write one number above the other with the places lined up. Run a finger along from the left and stop at the first column where the digits are different.

Try four practice questions

Real 2nd grade questions from our question bank, easiest first. Answer them right here, check each one, and see a worked solution for any question.

1Warm-up
Carlos wants to write 743 in expanded form. Carlos wrote:
$\displaystyle 743 = 7 + 40 + 3$
Select the statement that best describes Carlos's work.
A
All three place values are correct.
B
The hundreds place value is wrong.
C
The tens place value is wrong.
D
The ones place value is wrong.
Show the answer and how to solve it
The hundreds place is wrong. The 7 in 743 is in the hundreds place, so it is worth 700, not 7. The correct expanded form of 743 is $700 + 40 + 3$ .
1. 1First, find each place in 743. The 7 is in the hundreds place (worth 700). The 4 is in the tens place (worth 40). The 3 is in the ones place (worth 3).
2. 2Now check each part of Carlos's work: $7 + 40 + 3$ . The first part 7 does not match the hundreds — 7 hundreds is 700, not 7. The middle part 40 matches the tens (4 tens is 40). The last part 3 matches the ones (3 ones is 3).
3. 3The hundreds place is wrong. Carlos wrote 7 in the first part, but the 7 in 743 is in the hundreds place, so it should be 700. The correct expanded form is:
Common mistake. A common mistake is confusing the digit with its place value — the 7 in the hundreds place is worth 700, not 7. Always check which place a digit is in before writing its value.
The idea underneath. Each digit's value depends on its place. The same digit is worth digit times 100 in the hundreds place, digit times 10 in the tens place, or just the digit in the ones place.
2On level
Select the expanded form of the number shown.
$\displaystyle 23{,}605$
A
$\displaystyle 20{,}000 + {}$
$\displaystyle 3{,}000 + {}$
$\displaystyle 6 + {}$
$\displaystyle 5$
B
$\displaystyle 20{,}000 + {}$
$\displaystyle 3{,}000 + {}$
$\displaystyle 60 + {}$
$\displaystyle 5$
C
$\displaystyle 20{,}000 + {}$
$\displaystyle 3{,}000 + {}$
$\displaystyle 600 + {}$
$\displaystyle 5$
D
$\displaystyle 20{,}000 + {}$
$\displaystyle 3{,}000 + {}$
$\displaystyle 5$
Show the answer and how to solve it
The expanded form of $23{,}605$ is $20{,}000 + 3{,}000 + 600 + 5$ . The $0$ in the tens place is left out because it adds $0$ .
1. 1Look at each digit in $23{,}605$ and name its place value. Reading left to right: $2$ is in the ten thousands place, $3$ is in the thousands place, $6$ is in the hundreds place, $0$ is in the tens place, and $5$ is in the ones place.
2. 2Multiply each digit by its place value to find each part.
3. 3Add the nonzero place-value parts. The tens digit is $0$ , so we leave that part out — adding $0$ would not change anything.
Common mistake. A common mistake is writing the digit itself instead of its place-value part — for example, writing $+ 6$ for the hundreds digit instead of $+ 600$ . Another is forgetting to leave out the $0$ tens digit and including a $+ 0$ term, or skipping the hundreds digit entirely because of the nearby $0$ .
The idea underneath. In a multi-digit number, a digit's value depends on its place. The same digit $6$ can mean $6$ , $60$ , $600$ , $6{,}000$ , or $60{,}000$ — depending on which place it sits in.
3On level
Write 708 in expanded form.
708 =
+
+
Show the answer and how to solve it
The expanded form of 708 is $700 + 0 + 8$ . The digit 7 in the hundreds place stands for 700, the digit 0 in the tens place stands for 0, and the digit 8 in the ones place stands for 8.
1. 1Look at the digit in each place of 708.
2. 2The hundreds digit is 7. Because it is in the hundreds place, its value is 700.
3. 3The tens digit is 0. Because it is in the tens place, its value is 0.
4. 4The ones digit is 8. Because it is in the ones place, its value is 8.
5. 5Write the three place values with plus signs between them:
Common mistake. A common mistake is writing the digits without applying their place values, like $7 + 0 + 8$ . The 7 in 708 is in the hundreds place, so it stands for 700, not 7. Another common error is skipping the zero entirely and writing only $700 + 8$ in two boxes — but expanded form keeps a part for every place, including a 0 for the tens place.
The idea underneath. Each digit's value depends on its place. The same digit means a different amount in different places: a 3 in the hundreds place stands for 300, but a 3 in the tens place stands for 30, and a 3 in the ones place stands for just 3. A 0 in any place still keeps that place — it stands for 0 of those, not nothing.
4Stretch
Write the standard form of this number: "nine hundred eight thousand seventy-six."
Type only digits — do not type any commas.
Show the answer and how to solve it
Answer. 908076
The standard form is $908076$ . The first $0$ holds the tens place of the thousands period, and the second $0$ holds the hundreds place of the ones period.
1. 1Break the number name into periods. The thousands period is "nine hundred eight thousand," and the ones period is "seventy-six."
2. 2Write the thousands period as digits. "Nine hundred eight" means $9$ hundreds, $0$ tens, and $8$ ones. The tens slot has no tens named, so it is filled with $0$ , giving $908$ .
3. 3Write the ones period as digits. "Seventy-six" means $7$ tens and $6$ ones. No hundreds are named, so the hundreds slot is filled with $0$ , making the ones period $076$ .
4. 4Put the two periods together: $908$ followed by $076$ is $908{,}076$ , or $908076$ in digits only.
Common mistake. A common mistake is writing $90876$ (dropping one zero) instead of $908076$ . "Seventy-six" has no hundreds, so the hundreds slot of the ones period must be filled with $0$ , giving $076$ , not $76$ .
The idea underneath. Every period (ones, thousands) has exactly three digit slots: hundreds, tens, ones. When the number name leaves part of a period unsaid, fill those slots with $0$ to keep each period three digits long.