Hundreds, Tens, Ones and Tenths Worksheets for Grade 2 Students

Complete collection of worksheets with 20 practice exercises covering decimal place value identification, number composition, expanded form, and visual representations for grade 2 students.

Worksheets Part 1: Basic Place Value (Problems 1-10)
1 Identify place values
Problem 1
Circle the tenths digit in 4.7.
Definition:

Decimal place value positions: From left of decimal: ones, from right of decimal: tenths.

ONES
4
TENTHS
7
Step 1: Identify positions

Before decimal: 4 (ones), after decimal: 7 (tenths)

Step 2: Locate tenths digit

The tenths digit is the first digit after the decimal point

Step 3: Circle the answer

Circle the digit 7

Answer:

The tenths digit in 4.7 is 7.

2 Calculate place values
Problem 2
What is the value of the tenths digit in 3.8?
Definition:

Decimal digit value: The actual worth of a digit based on its position (digit × place value).

ONES
3 × 1 = 3
TENTHS
8 × 0.1 = 0.8
Step 1: Identify the tenths digit

In 3.8, the tenths digit is 8

Step 2: Calculate its value

Tenths value = 8 × 0.1 = 0.8

Answer:

The value of the tenths digit in 3.8 is 0.8.

3 Expanded form with decimals
Problem 3
Write 2.6 in expanded form.
Definition:

Decimal expanded form: Writing a number as the sum of each digit's value including decimal places.

ONES
2 × 1 = 2
TENTHS
6 × 0.1 = 0.6
Step 1: Break down each digit

2 is in the ones place: 2 × 1 = 2

6 is in the tenths place: 6 × 0.1 = 0.6

Step 2: Write in expanded form

2.6 = 2 + 0.6

2.6 = 2 + 0.6
Answer:

2.6 = 2 + 0.6

4 Ordering decimals
Problem 4
Put these numbers in order from least to greatest: 1.3, 1.8, 1.1
Definition:

Decimal ordering: Compare numbers by examining digits from left to right, including decimal places.

1.3
1|3
1.8
1|8
1.1
1|1
Step 1: Compare ones place first

All have 1 ones → Equal so far

Step 2: Compare tenths place

1.1: 1 tenth, 1.3: 3 tenths, 1.8: 8 tenths

So 1.1 < 1.3 < 1.8

Answer:

1.1, 1.3, 1.8

5 Decimal composition
Problem 5
What number is made up of 3 ones and 5 tenths?
Definition:

Decimal number composition: Building a number from its place value components including decimals.

3 ONES
3 × 1 = 3
5 TENTHS
5 × 0.1 = 0.5
Step 1: Convert each component to its value

3 ones = 3 × 1 = 3

5 tenths = 5 × 0.1 = 0.5

Step 2: Add all values together

3 + 0.5 = 3.5

Answer:

The number is 3.5.

6 Compare decimal values
Problem 6
Which is greater: 2.4 or 2.04?
Definition:

Decimal comparison: Compare numbers by examining digits from left to right, adding zeros if needed.

2.4
2|4|0
2.04
2|0|4
Step 1: Compare ones place

Both have 2 ones → Equal so far

Step 2: Compare tenths place

2.4 has 4 tenths, 2.04 has 0 tenths

Since 4 > 0, 2.4 > 2.04

Answer:

2.4 is greater than 2.04.

7 Decimal place value
Problem 7
What is the value of each digit in 5.7?
Definition:

Decimal digit values: Calculate the value of each digit based on its position including decimal places.

ONES
5 × 1 = 5
TENTHS
7 × 0.1 = 0.7
Step 1: Identify each digit and its position

5 in ones place, 7 in tenths place

Step 2: Calculate each digit's value

5 × 1 = 5

7 × 0.1 = 0.7

Answer:

Ones value: 5, Tenths value: 0.7

8 Visual representation
Problem 8
Show 1.4 using base ten blocks and tenths pieces.
Definition:

Decimal visual representation: Using base ten blocks and tenths pieces to model decimal numbers.

1
0.1
0.1
0.1
0.1
Step 1: Break down 1.4 by place value

1 one: 1 × 1 = 1

4 tenths: 4 × 0.1 = 0.4

Step 2: Represent with blocks

1 one block (unit)

4 tenths pieces (each 0.1)

Answer:

1 one block and 4 tenths pieces

9 Decimal subtraction
Problem 9
Subtract: 3.7 - 1.2
Definition:

Decimal subtraction: Subtracting numbers with tenths by working with ones and tenths separately.

ONES
3 - 1 = 2
TENTHS
7 - 2 = 5
Step 1: Align numbers by decimal point

3.7

- 1.2

-----

Step 2: Subtract tenths place

7 - 2 = 5

Step 3: Subtract ones place

3 - 1 = 2

Answer:

3.7 - 1.2 = 2.5

10 Decimal addition
Problem 10
Add: 2.3 + 1.6
Definition:

Decimal addition: Adding numbers with tenths by working with ones and tenths separately.

ONES
2 + 1 = 3
TENTHS
3 + 6 = 9
Step 1: Align numbers by decimal point

2.3

+ 1.6

-----

Step 2: Add tenths place

3 + 6 = 9

Step 3: Add ones place

2 + 1 = 3

Answer:

2.3 + 1.6 = 3.9

Worksheets Part 2: Advanced Problems (Problems 11-20)
11 Compare mixed numbers
Problem 11
Which is greater: 4.5 or 4?
Definition:

Mixed comparison: Comparing whole numbers and decimals by adding decimal places if needed.

4.5
4|5
4.0
4|0
Step 1: Compare ones place

Both have 4 ones → Equal so far

Step 2: Compare tenths place

4.5 has 5 tenths, 4.0 has 0 tenths

Since 5 > 0, 4.5 > 4.0

Answer:

4.5 is greater than 4.

12 Decimal word problem
Problem 12
Sarah has 2.3 meters of ribbon. She buys 1.7 more meters. How much ribbon does she have now?
Definition:

Decimal word problems: Translating story problems into decimal operations.

Step 1: Identify the operation

"Buys more" indicates addition: 2.3 + 1.7

ONES
2 + 1 = 3
TENTHS
3 + 7 = 10 → Write 0, carry 1
Step 2: Add tenths place

3 + 7 = 10 → Write 0, carry 1 to ones

Step 3: Add ones place

2 + 1 + 1 (carry) = 4

Answer:

Sarah has 4.0 meters of ribbon.

13 Decimal subtraction word problem
Problem 13
Tom had 5.6 liters of water. He drank 2.4 liters. How much water does he have left?
Definition:

Decimal subtraction word problem: Translating story problems into decimal subtraction.

Step 1: Identify the operation

"Drank" indicates subtraction: 5.6 - 2.4

ONES
5 - 2 = 3
TENTHS
6 - 4 = 2
Step 2: Subtract tenths place

6 - 4 = 2

Step 3: Subtract ones place

5 - 2 = 3

Answer:

Tom has 3.2 liters of water left.

14 Decimal pattern recognition
Problem 14
Complete the pattern: 0.2, 0.4, 0.6, __, __
Definition:

Decimal patterns: Identifying the rule by finding the difference between consecutive numbers.

Step 1: Find the pattern

0.4 - 0.2 = 0.2

0.6 - 0.4 = 0.2

The pattern is adding 0.2 each time

Step 2: Continue the pattern

0.6 + 0.2 = 0.8

0.8 + 0.2 = 1.0

Answer:

The next two numbers are 0.8 and 1.0.

15 Decimal equation solving
Problem 15
Find the missing number: 3.8 - __ = 1.5
Definition:

Decimal missing number problems: Using inverse operations to find unknown values.

Step 1: Set up the equation

3.8 - ? = 1.5

This means ? = 3.8 - 1.5

ONES
3 - 1 = 2
TENTHS
8 - 5 = 3
Step 2: Perform the subtraction

3.8 - 1.5 = 2.3

Step 3: Verify

3.8 - 2.3 = 1.5 ✓

Answer:

The missing number is 2.3.

16 Decimal addition with regrouping
Problem 16
Add: 2.8 + 1.7
Definition:

Decimal regrouping: When the sum in any place is 10 or more, carry over to the next place value.

Step 1: Align numbers by decimal point

2.8

+ 1.7

-----

ONES
2 + 1 + 1 (carry) = 4
TENTHS
8 + 7 = 15 → Write 5, carry 1
Step 2: Add tenths place

8 + 7 = 15 → Write 5, carry 1 to ones

Step 3: Add ones place

2 + 1 + 1 (carry) = 4

Answer:

2.8 + 1.7 = 4.5

17 Decimal subtraction with borrowing
Problem 17
Subtract: 4.2 - 1.8
Definition:

Decimal borrowing: When the top digit is smaller than the bottom digit, borrow from the next higher place value.

Step 1: Check tenths place

2 < 8, so borrow from ones: 4.2 → 3.[12]

ONES
3 - 1 = 2
TENTHS
12 - 8 = 4
Step 2: Subtract tenths place

12 - 8 = 4

Step 3: Subtract ones place

3 - 1 = 2

Answer:

4.2 - 1.8 = 2.4

18 Ordering with zeros
Problem 18
Put these numbers in order from greatest to least: 3.0, 3.1, 2.9
Definition:

Decimal ordering: Compare numbers by examining digits from left to right, including zeros.

3.0
3|0
3.1
3|1
2.9
2|9
Step 1: Compare ones place first

3.0 and 3.1 have 3 ones, 2.9 has 2 ones

So 2.9 is smallest

Step 2: Compare 3.0 and 3.1

Both have 3 ones, compare tenths: 3.1 has 1 tenth, 3.0 has 0 tenths

So 3.1 > 3.0

Answer:

3.1, 3.0, 2.9

19 Decimal place value challenge
Problem 19
What is the difference between the value of the ones digit and the tenths digit in 4.7?
Definition:

Decimal digit value difference: Calculate the value of each specified digit and find the difference.

Step 1: Identify the digits

Ones digit: 4, Tenths digit: 7

ONES VALUE
4 × 1 = 4
TENTHS VALUE
7 × 0.1 = 0.7
Step 2: Calculate the difference

4 - 0.7 = 3.3

Answer:

The difference is 3.3.

20 Mixed decimal operations
Problem 20
Calculate: 2.5 + 1.3 - 0.8
Definition:

Mixed decimal operations: Perform operations from left to right following order of operations.

Step 1: Perform addition first

2.5 + 1.3 = 3.8

Step 2: Perform subtraction next

3.8 - 0.8 = 3.0

AFTER ADDITION
3.8
AFTER SUBTRACTION
3.0
Answer:

2.5 + 1.3 - 0.8 = 3.0

Decimal Place Value Concepts Review
Tenths = Digit × 0.1
Decimal Place Value Formula
ONES PLACE
1
Left of decimal point
Value = Digit × 1
TENTHS PLACE
0.1
First after decimal point
Value = Digit × 0.1
Key Grade 2 Decimal Concepts:

Decimal point: The dot that separates whole numbers from fractional parts

Tenths: The first digit after the decimal point, representing parts of 1/10

Decimal numbers: Numbers that include a decimal point

Decimal place value: The value of a digit based on its position relative to the decimal point

Grade 2 Decimal Methods:
  1. Identify decimal positions: Before decimal (ones), after decimal (tenths)
  2. Determine decimal values: Multiply digit by its decimal place value
  3. Compare decimals: Start comparing from left of decimal
  4. Add decimals: Align decimal points and add each place separately
  5. Subtract decimals: Align decimal points and subtract each place separately
Tip 1: Always align decimal points when adding or subtracting.
Tip 2: Tenths are 10 times smaller than ones (0.1 = 1/10).
Tip 3: Add zeros to make comparison easier (2.3 = 2.30).
Tip 4: When comparing, start with the leftmost digit (highest place value).
Common errors for Grade 2: Misaligning decimal points during operations, confusing tenths with hundredths, forgetting that tenths are 1/10 of a whole.
Grade 2 learning tips: Practice with visual aids like fraction bars, use decimal grids, work with real-life examples like money.
Grade 2 Decimal Rules:

• Decimal alignment: Always line up decimal points when performing operations

• Place value rule: Digit × Place value gives actual value

• Comparison rule: Start comparing from highest place value

• Regrouping rule: 10 tenths = 1 one

• Order of operations: Perform calculations from left to right

Basic Decimal Place Value

Identify decimal place values, write expanded form, basic number composition with tenths

Download PDF
Decimal Addition and Subtraction

Adding and subtracting decimals, regrouping with tenths, word problems

Download PDF
Decimal Comparison

Ordering decimals, comparing decimal values, zero in decimal places

Download PDF
Detailed Summary: Hundreds, Tens, Ones and Tenths Concepts for Grade 2
Key Concepts and Definitions:

Place value: The value of a digit based on its position in a number. Each position represents a power of 10.

Hundreds place: The third digit from the right, representing groups of 100.

Tens place: The second digit from the right, representing groups of 10.

Ones place: The rightmost digit before the decimal point, representing individual units.

Tenths place: The first digit after the decimal point, representing 1/10 of a unit.

Decimal point: The dot that separates whole numbers from fractional parts.

Expanded form: Writing a number as the sum of each digit's value including decimals.

Standard form: The normal way of writing numbers (e.g., 3.4).

Base ten blocks: Visual tools representing units (ones), rods (tens), flats (hundreds), and tenths pieces.

Regrouping: Exchanging between place values (10 tenths = 1 one).

Zero placeholder: Zero holds the place in a number but contributes 0 to the total value.

Core Rules and Principles:

• Position rule: From right of decimal: tenths; from left of decimal: ones, tens, hundreds

• Multiplication rule: Digit × Place value gives actual value

• Comparison rule: Start comparing from highest place value

• Zero rule: Zero holds place but adds no value

• Regrouping rule: 10 tenths = 1 one

• Order of operations: Perform calculations from left to right

• Decimal alignment: Always line up decimal points when performing operations

Step-by-Step Methods:
  1. Identifying place values: Count positions from decimal point (left: ones, tens, hundreds; right: tenths)
  2. Calculating digit values: Multiply digit by its place value (100, 10, 1, or 0.1)
  3. Writing expanded form: Express each digit's value as a sum including decimals
  4. Number comparison: Compare digits starting from the highest place value
  5. Number composition: Add place values to form the complete number
  6. Visual representation: Use base ten blocks and tenths pieces to model numbers
  7. Decimal addition: Align decimal points and add each place separately
  8. Decimal subtraction: Align decimal points and subtract each place separately
  9. Regrouping: Exchange between place values when needed
  10. Word problem solving: Identify operation and apply place value concepts
Examples (Simple to Advanced):

Basic: 2.3 = 2 ones, 3 tenths

Intermediate: 4.5 + 1.2 = 5.7

Advanced: 3.8 - 1.5 = 2.3 (decimal subtraction)

Challenge: 2.5 + 1.3 - 0.8 = 3.0 (mixed operations)

Tips and Tricks:

• Always align decimal points when adding or subtracting

• Remember: each place is 10 times greater than the place to its right

• When comparing, start with the leftmost digit (highest place value)

• Tenths are 1/10 of a whole unit (0.1 = 1/10)

• Practice with visual aids like fraction bars for better understanding

• Always check your work by adding back or verifying with expanded form

Common Pitfalls:

• Misaligning decimal points during operations

• Confusing tenths with hundredths (grade 2 focuses on tenths)

• Forgetting that tenths are 1/10 of a whole unit

• Starting comparisons from the wrong end (always start from highest place value)

• Forgetting to regroup when performing decimal operations

• Not maintaining decimal point alignment during calculations

Key Notes for Memorization:

• Memory aid: "Houses, Tents, Units, Tenths" - H (hundreds), T (tens), U (ones), Th (tenths)

• Value calculation: Always multiply the digit by its place value

• Comparison strategy: Highest place value determines which number is larger

• Zero function: Maintains number structure even when contributing zero value

• Regrouping concept: 10 of a smaller unit equals 1 of the next larger unit

• Visual learning: Use fraction bars to reinforce decimal concepts

• Verification: Always check your answer by adding or subtracting back

Questions & Answers

Question: My grade 2 child is learning decimals for the first time. How can I explain tenths?

Answer: Explain tenths using familiar concepts! A tenth is one part out of ten equal parts. Use a pizza cut into 10 slices - each slice is one tenth (0.1) of the whole pizza. Or think of a dollar divided into 10 dimes - each dime is one tenth of a dollar. In 2.3, the 3 in the tenths place means 3 tenths, or 3 out of 10 parts of a whole. Use visual aids like fraction bars or grids divided into 10 parts to help your child visualize tenths.

Question: Why do we need decimal points? Can't we just write 2.5 as 25?

Answer: The decimal point is very important! It separates the whole number part from the fractional part. In 2.5, we have 2 whole units and 5 tenths (half of a unit), which equals 2.5 total. If we wrote 25, that would be 25 whole units, which is much bigger! The decimal point tells us where the whole number ends and the parts begin. Without it, we couldn't tell the difference between 2.5 and 25!

Question: What are some effective activities for grade 2 students to master decimal place value concepts?

Answer: Try these engaging grade 2 activities:

  • Decimal grids: Shade parts of a 10-part grid to represent tenths
  • Fraction bars: Use manipulatives that show tenths visually
  • Money activities: Use dimes to represent tenths of a dollar
  • Number line activities: Show where decimal numbers fall on a number line
  • Decimal matching games: Match standard form to visual representations
  • Real-world applications: Measure lengths using rulers marked in tenths

These hands-on activities help students visualize abstract concepts and make learning fun!