Place Value Tenths and Hundredths Worksheets for Grade 4 Students

Complete worksheets with exercises on identifying tenths and hundredths place values, converting fractions to decimals, and comparing decimal values with detailed solutions.

Worksheet Activities: Tenths and Hundredths
Activity 1

Identify the value of underlined digits in decimal numbers up to hundredths place.

Example: In 0.74, the value of 7 is 7 tenths (0.7).

Activity 2

Convert fractions with denominators of 10 and 100 to decimal form.

Example: Convert 3/10 and 7/100 to decimal form.

Activity 3

Compare decimal numbers using tenths and hundredths place values.

Example: Which is greater: 0.52 or 0.50?

Activity 4

Write decimals in expanded form using tenths and hundredths.

Example: Write 0.47 as 4/10 + 7/100.

1 Decimal Place Value Identification
Exercise 1
In the number 0.83, what is the value of the digit 8? What is the value of the digit 3?
Definition:

Decimal place value: The value of a digit based on its position relative to the decimal point. Tenths: The first position after the decimal point (1/10). Hundredths: The second position after the decimal point (1/100).

Method:
  1. Identify the decimal point position
  2. Count positions to the right of the decimal point
  3. Recognize the place value of each position
  4. Multiply the digit by the value of its position
Ones
0
.
Tenths
8
Hundredths
3
8 tenths = 8/10 = 0.8
3 hundredths = 3/100 = 0.03
Step 1: Identify the position of digit 8

In 0.83, the digit 8 is in the tenths place

Step 2: Calculate the value of digit 8

Digit value = 8 × (1/10) = 8/10 = 0.8

Step 3: Identify the position of digit 3

In 0.83, the digit 3 is in the hundredths place

Step 4: Calculate the value of digit 3

Digit value = 3 × (1/100) = 3/100 = 0.03

8 × (1/10) = 0.8
3 × (1/100) = 0.03
Final answer:

The value of the digit 8 is 0.8 (eight tenths). The value of the digit 3 is 0.03 (three hundredths).

Applied rules:

• Decimal point reference: Everything to the right of the decimal point is fractional

• Tenths place: First position after decimal point, value = 1/10

• Hundredths place: Second position after decimal point, value = 1/100

Tip: Think of tenths as parts of a whole divided into 10 equal pieces.
2 Converting Fractions to Decimals
Exercise 2
Convert 7/10 and 4/100 to decimal form. Where do these digits appear in the place value chart?
Definition:

Fraction to decimal conversion: Changing a fraction to its decimal equivalent by dividing the numerator by the denominator.

Ones
0
.
Tenths
7
Hundredths
0
Ones
0
.
Tenths
0
Hundredths
4
7/10 = 0.7 (7 tenths)
4/100 = 0.04 (4 hundredths)
Step 1: Convert 7/10 to decimal

7 ÷ 10 = 0.7, which means 7 tenths

Step 2: Convert 4/100 to decimal

4 ÷ 100 = 0.04, which means 0 tenths and 4 hundredths

Step 3: Place in decimal chart

0.7: The 7 goes in the tenths place (0.70)

0.04: The 4 goes in the hundredths place (0.04)

7/10 = 0.7
4/100 = 0.04
Final answer:

7/10 = 0.7 (the 7 is in the tenths place). 4/100 = 0.04 (the 4 is in the hundredths place).

Applied rules:

• Denominator determines place: Denominator of 10 = tenths, denominator of 100 = hundredths

• Division method: Numerator ÷ Denominator gives decimal form

• Place alignment: Decimal places align with fraction denominators

Tip: The number of zeros in the denominator tells you how many decimal places to move.
Worksheet Content and Structure
Decimal Value = Digit × Place Value
Decimal Place Value Formula
Tenths Place
× 1/10
Value = Digit × 0.1
Hundredths Place
× 1/100
Value = Digit × 0.01
Fraction to Decimal
÷ Denominator
Decimal = Numerator ÷ Denominator
Decimal Comparison
Place by Place
Compare from Left to Right
Key definitions:

Decimal: A number that contains a decimal point, representing values between whole numbers.

Tenths: One-tenth of a whole (1/10 = 0.1).

Hundredths: One-hundredth of a whole (1/100 = 0.01).

Decimal Point: The dot that separates the whole number part from the fractional part.

Decimal Place Value Method:
  1. Locate the decimal point: Identify where the decimal point is positioned
  2. Identify position: Count positions to the right of the decimal point
  3. Apply formula: Multiply digit by place value (0.1 for tenths, 0.01 for hundredths)
Fraction to Decimal Conversion:
  1. Divide numerator by denominator: Perform the division operation
  2. Place the result: Put the result in the appropriate decimal place
  3. Verify the placement: Ensure the decimal aligns with the fraction's denominator
Tip 1: Each position to the right of the decimal point is 10 times smaller than the previous.
Tip 2: Tenths = 1 decimal place, Hundredths = 2 decimal places.
Tip 3: 10 tenths = 1 whole, 100 hundredths = 1 whole.
Tip 4: Think of money: dimes are tenths (10¢ = 1/10 of $1), pennies are hundredths (1¢ = 1/100 of $1).
Common errors: Confusing tenths and hundredths positions, forgetting to include leading zeros.
Memorization trick: "Tenths is bigger than hundredths" - tenths are closer to the decimal point.
Decimal Place Value System:

• Ones (1) - left of decimal point

• Tenths (0.1) - first position right of decimal point

• Hundredths (0.01) - second position right of decimal point

Decimal Comparison Rules:

• Left-to-right comparison: Compare digits from left to right

• Place value matters: A digit in tenths is greater than any digit in hundredths

• Equal whole parts: When whole numbers are equal, compare decimal parts

Download Worksheet PDF
Additional Worksheet Exercises
3 Decimal Comparison
Exercise 3
Which is greater: 0.62 or 0.602? Explain your reasoning using place value.
Definition:

Decimal comparison: Determining which decimal number is larger by comparing place values from left to right.

Ones
0
.
Tenths
6
Hundredths
2
Ones
0
.
Tenths
6
Hundredths
0
Step 1: Compare whole number parts

Both have 0 in the ones place, so we move to decimal parts

Step 2: Compare tenths place

Both have 6 in the tenths place, so we move to hundredths

Step 3: Compare hundredths place

0.62 has 2 in hundredths, 0.602 has 0 in hundredths

Since 2 > 0, 0.62 > 0.602

0.62 > 0.602
Final answer:

0.62 is greater than 0.602 because in the hundredths place, 2 > 0.

Applied rules:

• Left-to-right comparison: Always compare from left to right

• Place value priority: Higher place values determine the comparison first

• Equal parts continue: When parts are equal, continue to the next place

4 Real-world Application
Exercise 4
Sarah ran 0.75 miles and John ran 0.70 miles. Who ran farther? Show your work using place value.
Definition:

Real-world application: Using decimal place value to solve practical problems involving measurements.

Ones
0
.
Tenths
7
Hundredths
5
Ones
0
.
Tenths
7
Hundredths
0
Step 1: Compare whole number parts

Both have 0 in the ones place, so we move to decimal parts

Step 2: Compare tenths place

Both have 7 in tenths, so we move to hundredths

Step 3: Compare hundredths place

Sarah has 5 in hundredths, John has 0 in hundredths

Since 5 > 0, Sarah ran farther

Step 4: Conclusion

Sarah ran 0.75 miles, which is farther than John's 0.70 miles

0.75 > 0.70
Final answer:

Sarah ran farther because 0.75 is greater than 0.70.

Applied rules:

• Measurement comparison: Decimal place value applies to real-world measurements

• Place value priority: Hundredths place comparison determines the outcome

• Contextual interpretation: Apply mathematical results to real-world scenarios

5 Mixed Operations
Exercise 5
What is the total value of the tenths digit and the hundredths digit in 0.47?
Definition:

Mixed operations: Combining place value identification with arithmetic operations.

Ones
0
.
Tenths
4
Hundredths
7
Step 1: Identify the tenths digit

In 0.47, the tenths digit is 4

Value of tenths digit = 4 × (1/10) = 0.4

Step 2: Identify the hundredths digit

In 0.47, the hundredths digit is 7

Value of hundredths digit = 7 × (1/100) = 0.07

Step 3: Calculate the total value

Total value = 0.4 + 0.07 = 0.47

0.4 + 0.07 = 0.47
Final answer:

The total value of the tenths digit and the hundredths digit in 0.47 is 0.47.

Applied rules:

• Digit identification: Locate specific digits in their respective places

• Value calculation: Determine the value of each digit separately

• Arithmetic combination: Add values to find totals

Decimal Place Value Tenths and Hundredths Summary
Comprehensive Learning Summary

Definitions and Key Concepts

Decimal: A number that contains a decimal point, representing values between whole numbers.

Decimal Point: The dot (.) that separates the whole number part from the fractional part.

Tenths: The first position after the decimal point, representing 1/10 or 0.1 of a whole.

Hundredths: The second position after the decimal point, representing 1/100 or 0.01 of a whole.

Core Rules and Principles

Decimal Place Value Rule: Decimal Value = Digit × Place Value

Tenths Place: Value = Digit × 0.1 (or Digit × 1/10)

Hundredths Place: Value = Digit × 0.01 (or Digit × 1/100)

Decimal Comparison: Compare from left to right, starting with the highest place value.

Step-by-Step Methods

Decimal Place Value Identification:

  1. Locate the decimal point in the number
  2. Count positions to the right of the decimal point
  3. Identify the place value of each position (tenths, hundredths)
  4. Multiply the digit by its place value to get the actual value

Fraction to Decimal Conversion:

  1. Divide the numerator by the denominator
  2. Place the result in the appropriate decimal position
  3. Match the denominator to the decimal place (10 = tenths, 100 = hundredths)

Decimal Comparison:

  1. Compare whole number parts first
  2. If equal, compare tenths place
  3. If tenths are equal, compare hundredths place
  4. Continue to the right until a difference is found

Examples (Simple to Advanced)

Simple Example: In 0.5, the 5 is in the tenths place and has a value of 0.5 (5 × 0.1).

Intermediate Example: In 0.23, the 2 is in the tenths place (value = 0.2) and the 3 is in the hundredths place (value = 0.03).

Advanced Example: Comparing 0.75 and 0.70: Both have 0 in ones and 7 in tenths, but 0.75 has 5 in hundredths while 0.70 has 0 in hundredths, so 0.75 > 0.70.

Tips and Memory Aids

Money analogy: Think of tenths as dimes (10¢ = 0.10) and hundredths as pennies (1¢ = 0.01).

Size comparison: Each position to the right is 10 times smaller than the previous one.

Leading zeros: 0.5 = 0.50 = 0.500 - extra zeros don't change the value.

Common Mistakes to Avoid

Confusing tenths and hundredths: Remember tenths come first after the decimal point.

Incorrect comparison: Don't compare decimal numbers like whole numbers - always go left to right by place value.

Forgetting place value: Each digit's value depends on its position, not just the digit itself.

Key Takeaways for Memorization

• The decimal point is the key reference point for all decimal operations

• Each decimal place is 10 times smaller than the place to its left

• Tenths are larger than hundredths

• Practice with real-world examples (money, measurements) helps reinforce concepts

Decimal Value = Digit × Place Value
Core Formula
Tenths
1/10 = 0.1
First decimal place
Hundredths
1/100 = 0.01
Second decimal place
Comparison
Left to Right
Start with highest place
Key definitions:

Decimal: A number that contains a decimal point, representing values between whole numbers

Tenths: The first position after the decimal point (value = 1/10 or 0.1)

Hundredths: The second position after the decimal point (value = 1/100 or 0.01)

Complete methodology:
  1. Identify the decimal point: Locate where the decimal point is positioned
  2. Determine the position: Count positions to the right of the decimal point
  3. Recognize the place value: Know the value associated with each position
  4. Calculate the value: Multiply the digit by its place value
  5. Verify the answer: Ensure the calculated value makes logical sense
Tip 1: Think of money - dimes are tenths ($0.10), pennies are hundredths ($0.01).
Tip 2: Each position to the right is 10 times smaller than the position to its left.
Tip 3: When comparing decimals, go left to right by place value.
Tip 4: 10 tenths = 1 whole, 100 hundredths = 1 whole.
Common errors: Confusing tenths and hundredths positions, comparing decimals like whole numbers.
Memory aid: "Tenths are bigger than hundredths" - tenths are closer to the decimal point.
Decimal Place Value Rules:

• Decimal point reference: Everything to the right is fractional

• Position matters: Same digit has different values in different positions

• Right-to-left counting: Positions decrease in value going right from decimal

• Comparison principle: Compare from left to right by place value

Fraction to Decimal Rules:

• Denominator determines place: Denominator of 10 = tenths, 100 = hundredths

• Division method: Numerator ÷ Denominator gives decimal form

• Place alignment: Decimal places align with fraction denominators

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Questions & Answers

Question: I'm confused about tenths and hundredths. How do I remember which is which?

Answer: Here are some helpful ways to remember tenths and hundredths:

  • Position order: Tenths come first after the decimal point, then hundredths. Think "T comes before H" in the alphabet, just like tenths come before hundredths after the decimal.
  • Money analogy: Think of money - dimes are tenths of a dollar ($0.10) and pennies are hundredths of a dollar ($0.01).
  • Size comparison: Tenths are bigger than hundredths. Just like 1/10 is bigger than 1/100.

Examples:

  • In 0.3, the 3 is in the tenths place (3 tenths = 3/10)
  • In 0.03, the 3 is in the hundredths place (3 hundredths = 3/100)
  • 0.3 is 10 times larger than 0.03!

Remember: The closer a digit is to the decimal point, the larger its value!

Question: Why is 0.5 the same as 0.50? Shouldn't 0.50 be bigger since it has more digits?

Answer: This is a very common misconception! Adding zeros to the right of the last non-zero digit in a decimal doesn't change its value. Here's why:

  • 0.5 means 5 tenths (5/10)
  • 0.50 means 50 hundredths (50/100)
  • But 5/10 = 50/100! They are equivalent fractions.

Think of it like money: $0.50 (50 cents) is the same as $0.5 (50 cents written differently).

More examples:

  • 0.7 = 0.70 = 0.700 (all represent seven tenths)
  • 0.25 = 0.250 (twenty-five hundredths)
  • 2.3 = 2.30 = 2.300 (two and three tenths)

The number of digits doesn't determine size - the place value does!

Question: How do I compare decimals like 0.4 and 0.39? It seems like 0.39 should be bigger because it has more digits.

Answer: When comparing decimals, you must compare place by place from left to right, not by the number of digits! Let's compare 0.4 and 0.39 step by step:

  • Step 1: Compare ones place: Both have 0, so continue
  • Step 2: Compare tenths place: 0.4 has 4, 0.39 has 3
  • Step 3: Since 4 > 3, 0.4 > 0.39

You could also think of 0.4 as 0.40 (adding a zero doesn't change the value). Now it's clear: 0.40 > 0.39.

The rule for decimal comparison is: go from left to right, comparing digits in the same place value. The first difference determines which number is larger!

More examples:

  • 0.6 vs 0.59: 6 tenths > 5 tenths, so 0.6 > 0.59
  • 0.72 vs 0.719: 7 tenths = 7 tenths, 2 hundredths > 1 hundredth, so 0.72 > 0.719
  • 0.5 vs 0.499: 5 tenths > 4 tenths, so 0.5 > 0.499