Grade 2 · Place Value · MAT-02-PV-002
Hundreds, Tens, and Ones
Decompose three-digit numbers into hundreds, tens, and ones.
Learning objectives
What you should be able to do
- Decompose three-digit numbers into hundreds, tens, and ones.
- Compose a number from stated place-value units.
- Explain equivalences such as 1 hundred = 10 tens = 100 ones.
Prerequisite check
Make sure the foundation is ready.
Checks the place-value structure extended in this lesson.
Learn
Build the idea from meaning, not memorization.
Each place is ten times the place to its right
Ten ones can be bundled into one ten. Ten tens can be bundled into one hundred. This repeated factor-of-ten structure is what makes the base-ten system powerful.
A digit's value depends on its position
In 352, the digit 3 means 300 because it is in the hundreds place. The digit 5 means 50, and the digit 2 means 2 ones. The same digit can represent different values in different positions.
Numbers can be composed and decomposed
352 can be built as 3 hundreds + 5 tens + 2 ones. It can also be regrouped in equivalent ways, such as 2 hundreds + 15 tens + 2 ones. The total value stays the same.
Zero is a place holder with real meaning
In 507, zero tells us there are no tens. Without the zero, 57 would mean a completely different number.
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.
- build number
- trade hundred for tens
- trade ten for ones
- identify digit value
Worked examples
Twenty different ways to see the concept work.
Decompose 243.
2 hundreds + 4 tens + 3 onesRead each digit by place.
Value of 6 in 681.
600The 6 is in the hundreds place.
Value of 8 in 681.
80The 8 is in the tens place.
Value of 1 in 681.
1The 1 is in the ones place.
Compose 4 hundreds, 2 tens, 7 ones.
427Place each digit in its matching position.
Compose 5 hundreds, 0 tens, 9 ones.
509Zero records the empty tens place.
How many tens equal 1 hundred?
10 tensTen groups of ten make 100.
How many ones equal 1 hundred?
100 onesA hundred contains one hundred individual ones.
How many ones equal 3 tens?
30 onesEach ten contains 10 ones.
Regroup 2 hundreds as tens.
20 tensEach hundred is 10 tens.
Regroup 4 hundreds as ones.
400 onesEach hundred is 100 ones.
Can 326 be 2 hundreds,12 tens,6 ones?
YesThe equivalent values are 200, 120, and 6; together they total 326.
Can 326 be 3 hundreds,1 ten,16 ones?
Yes16 ones regroup as 1 ten 6 ones, giving 326.
Why is 507 not the same as 57?
507 has 5 hundredsPlace positions change the value.
Write 700 as hundreds,tens,ones.
7 hundreds,0 tens,0 onesZeros show empty lower places.
Write 90 as hundreds,tens,ones.
0 hundreds,9 tens,0 onesOnly tens are present.
Which is greater value: digit 4 in 452 or digit 4 in 245?
4 in 452It represents 400 versus 40.
A model has 6 hundred-flats,3 ten-rods,8 ones.
638Compose place values.
Trade 1 hundred-flat for ten-rods.
10 ten-rodsThis is an equivalent regrouping.
Explain why 1 hundred = 10 tens.
Both equal 100 onesThey are different bundles representing the same quantity.
Practice
Guided practice with hints
01Decompose 714.
Hint: Read each digit by place.
Answer: 7 hundreds,1 ten,4 ones
02Compose 3 hundreds,8 tens,2 ones.
Hint: Place the digits.
Answer: 382
03Value of 5 in 457?
Hint: Look at its place.
Answer: 50
04How many tens in 2 hundreds?
Hint: Each hundred is 10 tens.
Answer: 20
05Can 450 be 3 hundreds and 15 tens?
Hint: Compute 300+150.
Answer: Yes
06Why does 604 need the 0?
Hint: It records an empty place.
Answer: It shows zero tens and keeps 6 in the hundreds place.
Practice
Independent practice
01Decompose 936.
Answer: 9 hundreds,3 tens,6 ones
02Compose 8 hundreds,0 tens,5 ones.
Answer: 805
03Value of 7 in 274?
Answer: 70
04How many tens in 5 hundreds?
Answer: 50
05How many ones in 4 tens?
Answer: 40
06Can 512 be 4 hundreds,11 tens,2 ones?
Answer: Yes
07What does the 0 mean in 308?
Answer: 0 tens
08Which is larger: value of 3 in 305 or 530?
Answer: 3 in 305 (300 vs 30)
Common mistakes
Learn to catch the error, not just the answer.
Multiply the digit by its place unit: hundreds, tens, or ones.
Zero preserves the empty tens place and the positions of the other digits.
Trades such as 1 hundred for 10 tens are equivalent exchanges.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Represent a three-digit inventory count using boxes of 100, bundles of 10, and single items.
- Use play money or place-value blocks to exchange 10 tens for 1 hundred.
Challenge problems
List two decompositions of 364.
For example 3H+6T+4O and 2H+16T+4O.
How many ones are in 7 hundreds?
700
Why can 4 hundreds and 13 tens represent 530?
400+130=530.
Explain how zero functions differently as a digit and as 'nothing.'
A zero digit records that a particular place contains no units while preserving positional value.
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 6
Game mode
Base-Ten Trading Post
Build target numbers and make equivalent trades without changing total value.
Practice
Mastery check
01Decompose 425.
Answer: 4 hundreds,2 tens,5 ones
02Compose 6 hundreds,3 tens,9 ones.
Answer: 639
03How many tens equal 1 hundred?
Answer: 10
04How many ones equal 1 hundred?
Answer: 100
05Value of 8 in 184?
Answer: 80
06Can 245 be 1 hundred,14 tens,5 ones?
Answer: Yes
07What does 0 mean in 703?
Answer: Zero tens
08Explain why regrouping preserves value.
Answer: The exchanged units are equivalent, such as 10 tens = 1 hundred.
Terminology
Words to know
- place value
- The value a digit has because of its position in a numeral.
- compose
- Build a number from place-value parts.
- decompose
- Break a number into place-value parts.
- regroup
- Exchange equivalent base-ten units without changing total value.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Common Core State Standards for Mathematics — 2.NBT.A.1
Hundreds, tens, ones and base-ten equivalence.