Grade 2 · Place Value · MAT-02-PV-003
Standard, Word, and Expanded Form
Convert among standard form, word form, and expanded form for numbers to 1000.
Learning objectives
What you should be able to do
- Convert among standard form, word form, and expanded form for numbers to 1000.
- Explain how expanded form records the value of each digit.
- Use place-value reasoning to detect mismatched representations.
Prerequisite check
Make sure the foundation is ready.
Checks understanding needed for expanded form.
Learn
Build the idea from meaning, not memorization.
Standard form is the usual numeral
Standard form writes a number using digits in place-value positions, such as 582.
Expanded form shows each digit's value
582 can be written 500 + 80 + 2. Expanded form makes the hidden place values visible and helps explain arithmetic and comparison.
Word form names the same structure
582 is read five hundred eighty-two. Word form and expanded form are two different ways to express the same place-value composition.
Zeros affect what appears in expanded form
In 604, the tens place has zero tens, so expanded form is commonly written 600 + 4. The missing 0 tens term is understood, but the zero remains essential in standard form.
Interactive math lab
Change it. See what stays true.
Base-Ten Lab
Change hundreds, tens, and ones and watch the total rebuild from place value.
- model to standard
- standard to expanded
- word to model
- spot mismatch
Worked examples
Twenty different ways to see the concept work.
Expand 321.
300+20+1Use each digit's place value.
Write 300+20+1 in standard form.
321Combine hundreds,tens,ones.
Write 321 in words.
three hundred twenty-oneRead place values.
Expand 507.
500+7There are zero tens.
Write 'eight hundred four.'
8048 hundreds,0 tens,4 ones.
Expand 990.
900+90Zero ones add no value.
Standard form of 700+60+5.
765Combine place-value parts.
Word form of 440.
four hundred forty4 hundreds and 4 tens.
Expanded form of 1000.
1000It is a single thousand unit at this level.
Which matches 246: 200+40+6 or 20+400+6?
200+40+6Each digit must have the correct positional value.
Does 305 match 300+50?
No300+50=350.
Does 305 match 300+5?
YesThere are 3 hundreds,0 tens,5 ones.
Write 618 in three forms.
618; six hundred eighteen; 600+10+8All representations agree.
Word form 'nine hundred ninety-nine' in expanded form.
900+90+9Translate each place.
Standard form of 'two hundred thirty.'
2302 hundreds,3 tens,0 ones.
Expand 402.
400+2Zero tens are omitted from the sum.
Why isn't 402 equal 40+2?
40+2=42The 4 is worth 400 in 402.
Which form best exposes the value of the 7 in 273?
Expanded: 200+70+3It shows 70 explicitly.
Correct mismatch: 451 = 400+5+1.
400+50+1The 5 is in the tens place.
Explain why all three forms can name the same number.
They encode identical place-value quantities in different representationsRepresentation changes, value does not.
Practice
Guided practice with hints
01Expand 734.
Hint: Write hundreds+tens+ones.
Answer: 700+30+4
02Standard form of 600+20+9.
Hint: Combine places.
Answer: 629
03Word form of 508.
Hint: Remember zero tens are not spoken as 'zero tens.'
Answer: five hundred eight
04Does 470 equal 400+70?
Hint: Add the parts.
Answer: Yes
05Fix 286 = 200+8+6.
Hint: The 8 is in tens place.
Answer: 200+80+6
06Write 903 in all three forms.
Hint: Use place value.
Answer: 903; nine hundred three; 900+3
Practice
Independent practice
01Expand 615.
Answer: 600+10+5
02Standard form 900+80+2.
Answer: 982
03Word form of 740.
Answer: seven hundred forty
04Standard form of 'three hundred six.'
Answer: 306
05Expand 808.
Answer: 800+8
06Does 521=500+20+1?
Answer: Yes
07Fix 364=300+6+4.
Answer: 300+60+4
08Write 999 in expanded form.
Answer: 900+90+9
Common mistakes
Learn to catch the error, not just the answer.
Translate each digit into hundreds, tens, or ones before adding.
The middle digit is zero; 504=500+4.
Check that each form encodes the same place-value amounts.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Read an address or inventory number and write it in word and expanded forms.
- Use expanded form to explain why two three-digit numerals differ.
Challenge problems
Find a number whose expanded form is 800+30+0.
830
Why can 600+0+4 be simplified to 600+4?
Adding zero changes nothing.
Create an incorrect expanded form for 572, then explain the error.
Example 500+7+2; the 7 should represent 70.
How does expanded form help with addition?
It separates numbers into place-value parts that can be combined systematically.
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 6
Game mode
Three-Form Match
Match standard, word, expanded, and base-ten representations of the same number.
Practice
Mastery check
01Expand 482.
Answer: 400+80+2
02Standard form of 700+5.
Answer: 705
03Word form of 319.
Answer: three hundred nineteen
04Does 406=400+6?
Answer: Yes
05Fix 253=200+5+3.
Answer: 200+50+3
06Write 870 in expanded form.
Answer: 800+70
07Write 'six hundred two' as numeral.
Answer: 602
08Explain expanded form.
Answer: It writes a number as the sum of each digit's place value.
Terminology
Words to know
- standard form
- The usual way of writing a number with digits.
- word form
- A number written using number words.
- expanded form
- A number written as the sum of its place values.
- representation
- A way to show the same mathematical quantity.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Common Core State Standards for Mathematics — 2.NBT.A.3
Reading/writing numbers to 1000 using numerals, names, and expanded form.