Decimal to Fraction Practice Worksheet for 4th Grade Students

Comprehensive practice worksheet covering decimal to fraction conversion from tenths to hundred-thousands. Includes 10 exercises with detailed solutions and study guide.

Practice Worksheet Problems
Basic Conversions (Problems 1-5)
1 0.3
2 0.75
3 0.2
4 0.5
5 0.125
Intermediate Conversions (Problems 6-8)
6 0.875
7 0.04
8 0.625
Advanced Conversions (Problems 9-10)
9 2.25
10 0.008
1 Problem Solutions
Solutions Guide
Detailed step-by-step solutions for all worksheet problems.
Solution Method:

Decimal place value: Count decimal places, write as fraction, simplify to lowest terms.

Step-by-Step Process:
  1. Count decimal places
  2. Write decimal digits as numerator over appropriate power of 10
  3. Find GCD of numerator and denominator
  4. Divide both by GCD to get simplest form
  5. Verify by dividing numerator by denominator
Problem 1: Convert 0.3

Decimal places: 1 → denominator = 10

0.3 = 3/10 (already in simplest form since GCD(3,10) = 1)

Problem 2: Convert 0.75

Decimal places: 2 → denominator = 100

0.75 = 75/100

GCD(75,100) = 25

75÷25 = 3, 100÷25 = 4

So 0.75 = 3/4

Problem 3: Convert 0.2

Decimal places: 1 → denominator = 10

0.2 = 2/10

GCD(2,10) = 2

2÷2 = 1, 10÷2 = 5

So 0.2 = 1/5

Problem 4: Convert 0.5

Decimal places: 1 → denominator = 10

0.5 = 5/10

GCD(5,10) = 5

5÷5 = 1, 10÷5 = 2

So 0.5 = 1/2

Problem 5: Convert 0.125

Decimal places: 3 → denominator = 1000

0.125 = 125/1000

GCD(125,1000) = 125

125÷125 = 1, 1000÷125 = 8

So 0.125 = 1/8

Problem 6: Convert 0.875

Decimal places: 3 → denominator = 1000

0.875 = 875/1000

GCD(875,1000) = 125

875÷125 = 7, 1000÷125 = 8

So 0.875 = 7/8

Problem 7: Convert 0.04

Decimal places: 2 → denominator = 100

0.04 = 4/100

GCD(4,100) = 4

4÷4 = 1, 100÷4 = 25

So 0.04 = 1/25

Problem 8: Convert 0.625

Decimal places: 3 → denominator = 1000

0.625 = 625/1000

GCD(625,1000) = 125

625÷125 = 5, 1000÷125 = 8

So 0.625 = 5/8

Problem 9: Convert 2.25

Separate: 2 + 0.25

Convert decimal part: 0.25 = 25/100 = 1/4

Combine: 2 + 1/4 = 2 1/4

Problem 10: Convert 0.008

Decimal places: 3 → denominator = 1000

0.008 = 8/1000

GCD(8,1000) = 8

8÷8 = 1, 1000÷8 = 125

So 0.008 = 1/125

Final Answers:

1. 0.3 = 3/10

2. 0.75 = 3/4

3. 0.2 = 1/5

4. 0.5 = 1/2

5. 0.125 = 1/8

6. 0.875 = 7/8

7. 0.04 = 1/25

8. 0.625 = 5/8

9. 2.25 = 2 1/4

10. 0.008 = 1/125

Decimal to Fraction Study Guide
Decimal Places → Denominator
Place Value Rule
Tenths
0.d = d/10
1 decimal place = denominator 10
Hundredths
0.dd = dd/100
2 decimal places = denominator 100
Thousandths
0.ddd = ddd/1000
3 decimal places = denominator 1000
Ten-Thousandths
0.dddd = dddd/10000
4 decimal places = denominator 10000
Key Definitions:

Decimal: A number that uses a decimal point to separate the whole number part from the fractional part

Fraction: A number representing a part of a whole, expressed as numerator/denominator

Place Value: The value of a digit based on its position in a number

Simplest Form: A fraction reduced to lowest terms where numerator and denominator have no common factors except 1

GCD (Greatest Common Divisor): The largest number that divides both numerator and denominator evenly

Complete Methodology:
  1. Analyze the decimal: Count how many digits are after the decimal point
  2. Identify the place value: Determine if it's tenths, hundredths, thousandths, etc.
  3. Write the fraction: Use the digits as numerator, denominator based on place value
  4. Simplify: Reduce to lowest terms by dividing by GCD
  5. Verify: Divide numerator by denominator to check accuracy
Tip 1: Remember the decimal place value pattern: 1 place = 10, 2 places = 100, 3 places = 1000, 4 places = 10000.
Tip 2: Leading zeros still count: 0.05 has 2 decimal places, so denominator is 100.
Tip 3: For mixed numbers, convert decimal part separately then combine with whole number.
Tip 4: Always verify your answer by dividing numerator by denominator.
Common Errors: Miscounting decimal places, forgetting to simplify fractions, not accounting for leading zeros.
Worksheet Preparation: Practice conversions up to thousandths, memorize common fractions, verify all answers.
Essential Formulas:

• n decimal places → denominator = 10^n

• Simplification: Divide by GCD(numerator, denominator)

• Verification: numerator ÷ denominator should equal original decimal

• Mixed number: Whole part + (decimal part converted to fraction)

Additional Practice Exercises
A Extra Practice Problems
Additional Problems
More practice problems to reinforce your understanding.
A1 0.6
A2 0.4
A3 0.9
A4 0.05
A5 0.375
A6 1.5
A7 0.005
A8 0.08
Answer Key:

A1. 0.6 = 3/5

A2. 0.4 = 2/5

A3. 0.9 = 9/10

A4. 0.05 = 1/20

A5. 0.375 = 3/8

A6. 1.5 = 1 1/2

A7. 0.005 = 1/200

A8. 0.08 = 2/25

B Challenge Problems
Challenge Problems
Advanced problems for extra practice.
C1 0.0001
C2 4.0625
C3 0.016
C4 0.1875
Challenge Answers:

C1. 0.0001 = 1/10000

C2. 4.0625 = 4 1/16

C3. 0.016 = 2/125

C4. 0.1875 = 3/16

Comprehensive Study Summary
Decimal ↔ Fraction Conversion
Core Concept
Key Definitions:

Decimal Place Value: Each position after the decimal point represents a specific fraction of 1

Tenths: 1 decimal place (0.1 = 1/10)

Hundredths: 2 decimal places (0.01 = 1/100)

Thousandths: 3 decimal places (0.001 = 1/1000)

Ten-Thousandths: 4 decimal places (0.0001 = 1/10000)

Hundred-Thousandths: 5 decimal places (0.00001 = 1/100000)

Complete Conversion Process:
  1. Count decimal places: Determine how many digits come after the decimal point
  2. Write initial fraction: Use decimal digits as numerator, denominator as 10^places
  3. Find GCD: Greatest Common Divisor of numerator and denominator
  4. Divide both parts: by GCD to get simplest form
  5. Verify result: Divide numerator by denominator to confirm
Pattern Recognition: 1 place = 10, 2 places = 100, 3 places = 1000, 4 places = 10000, 5 places = 100000
Leading Zeros: Still count: 0.05 = 5/100 (not 5/10)
Common Conversions: 0.5 = 1/2, 0.25 = 1/4, 0.75 = 3/4, 0.125 = 1/8, 0.625 = 5/8
Verification: Always divide numerator by denominator to check your answer
Common Mistakes: Miscounting decimal places, forgetting to simplify, not accounting for leading zeros, incorrect GCD calculation.
Memory Aids: "Decimal places = zeros after 1 in denominator", "Always simplify to lowest terms", "Check with division".
Essential Conversion Rules:

• n decimal places → denominator = 10^n

• Always express in simplest form by dividing by GCD

• For mixed numbers, convert decimal part separately

• Leading zeros count in decimal places: 0.05 has 2 places

• Verify by dividing numerator by denominator

Decimal to Fraction Conversion Guide

Visual Conversion Guide

Place Value System

0.1 = One Tenth = 1/10

0.01 = One Hundredth = 1/100

0.001 = One Thousandth = 1/1000

0.0001 = One Ten-Thousandth = 1/10000

0.00001 = One Hundred-Thousandth = 1/100000

Conversion Process

Step 1: Count decimal places

Step 2: Write digits over appropriate power of 10

Step 3: Simplify by GCD

Step 4: Verify by division

Conversion Workflow
1
Count Digits
2
Set Denominator
3
Simplify
4
Verify
Decimal-Fraction Relationships

0.1 ↔ 1/10

0.25 ↔ 1/4

0.5 ↔ 1/2

0.75 ↔ 3/4

0.125 ↔ 1/8

0.625 ↔ 5/8

Remember: Count decimal places, use power of 10 as denominator, simplify to lowest terms!

Worksheet Help Q&A

Question: I'm having trouble with problems like 0.04. Why isn't it just 4/10?

Answer: Great question! The key is to count ALL digits after the decimal point, including zeros:

For 0.04:

  • Position 1 after decimal: 0 (tenths place)
  • Position 2 after decimal: 4 (hundredths place)
  • That's 2 digits total after the decimal point
  • So denominator = 100 (not 10)
  • Therefore: 0.04 = 4/100 = 1/25

The leading zero still counts as a decimal place! Think of it as 4 hundredths, not 4 tenths.

Question: How do I know when I've simplified a fraction completely? Like with 75/100 = 3/4, how do I know to stop there?

Answer: A fraction is in simplest form when the numerator and denominator have no common factors except 1. Here's how to check:

Method 1 - Factor Lists:

  • Factors of 3: 1, 3
  • Factors of 4: 1, 2, 4
  • Only common factor: 1
  • So 3/4 is in simplest form!

Method 2 - Prime Factorization:

  • 3 = 3 (prime)
  • 4 = 2²
  • No common prime factors
  • So 3/4 is in simplest form!

With practice, you'll quickly recognize when fractions are fully simplified.

Question: What if I have a problem like 2.25? Do I convert the whole number too?

Answer: No, you don't convert the whole number! For mixed numbers like 2.25, follow this process:

  • Separate the whole number from the decimal: 2.25 = 2 + 0.25
  • Convert only the decimal part: 0.25 = 25/100 = 1/4
  • Combine: 2 + 1/4 = 2 1/4

The whole number stays as it is, and only the decimal part gets converted to a fraction. This creates a mixed number!