Decimal to Fraction Conversion Practice for 4th Grade Students

Master decimal to fraction conversion with 5 detailed exercises covering tenths, hundredths, thousandths, and beyond. Comprehensive explanations, rules, and visual examples.

Solution: Exercises 1 to 3
1 Converting Tenths
Exercise 1
Convert 0.7 to a fraction.
🎯 Goal: Express the decimal as a fraction in simplest form.
Definition:

Decimal place value: 0.7 means 7 tenths, or 7 out of 10 equal parts.

Conversion method:
  1. Identify the number of decimal places
  2. Write the decimal digits as the numerator
  3. Write the denominator as 1 followed by zeros equal to decimal places
  4. Simplify if possible
Decimal
0.7
Fraction
7/10
Step 1: Identify decimal places

0.7 has 1 decimal place (the 7 is in the tenths place)

Step 2: Write as fraction

Numerator = 7, Denominator = 10 (because of 1 decimal place)

So 0.7 = 7/10

Step 3: Check for simplification

GCD(7,10) = 1, so 7/10 is already in simplest form

0.7 = 7/10
Final answer:

0.7 = 7/10

Applied rules:

• Decimal Place Value: Each position represents a power of 10

• Conversion Rule: Number of decimal places determines denominator (10, 100, 1000, etc.)

• Simplification: Reduce fraction by dividing by GCD

Tip: Remember: 1 decimal place = tenths (denominator 10), 2 decimal places = hundredths (denominator 100), 3 decimal places = thousandths (denominator 1000).
2 Converting Hundredths
Exercise 2
Convert 0.45 to a fraction.
🎯 Goal: Express the decimal as a fraction in simplest form.
Definition:

Decimal place value: 0.45 means 45 hundredths, or 45 out of 100 equal parts.

Decimal
0.45
Initial Fraction
45/100
Simplified
9/20
Step 1: Identify decimal places

0.45 has 2 decimal places (the 4 is in the tenths place, 5 in the hundredths place)

Step 2: Write as fraction

Numerator = 45, Denominator = 100 (because of 2 decimal places)

So 0.45 = 45/100

Step 3: Simplify the fraction

Find GCD(45,100): Factors of 45: 1,3,5,9,15,45. Factors of 100: 1,2,4,5,10,20,25,50,100

GCD(45,100) = 5

45÷5 = 9, 100÷5 = 20

So 45/100 = 9/20

0.45 = 9/20
Final answer:

0.45 = 9/20

Applied rules:

• Decimal Place Value: Each digit position represents its place value

• Simplification: Divide numerator and denominator by their greatest common divisor

• Verification: Check that 9÷20 = 0.45

Tip: Always simplify fractions to their lowest terms by finding the GCD of numerator and denominator.
3 Converting Thousandths
Exercise 3
Convert 0.125 to a fraction.
🎯 Goal: Express the decimal as a fraction in simplest form.
Definition:

Decimal place value: 0.125 means 125 thousandths, or 125 out of 1000 equal parts.

Decimal
0.125
Initial Fraction
125/1000
Simplified
1/8
Step 1: Identify decimal places

0.125 has 3 decimal places (the 1 is in the tenths place, 2 in the hundredths, 5 in the thousandths)

Step 2: Write as fraction

Numerator = 125, Denominator = 1000 (because of 3 decimal places)

So 0.125 = 125/1000

Step 3: Simplify the fraction

Find GCD(125,1000): Both are multiples of 125

125÷125 = 1, 1000÷125 = 8

So 125/1000 = 1/8

Step 4: Verify the result

1÷8 = 0.125 ✓

0.125 = 1/8
Final answer:

0.125 = 1/8

Applied rules:

• Place Value Rule: 3 decimal places = thousandths (denominator 1000)

• Simplification: Find the greatest common divisor to reduce fraction

• Verification: Divide numerator by denominator to check result

Tip: Common decimal-to-fraction conversions like 0.125 = 1/8 are worth memorizing for faster calculations.
Decimal to Fraction Conversion Rules
Decimal = Numerator/Denominator
Conversion Formula
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
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

Complete methodology:
  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. Simplify: Find GCD and divide both numerator and denominator
  4. Verify: Divide numerator by denominator to confirm result
Tip 1: Remember the pattern: 1 decimal = tenths (10), 2 decimals = hundredths (100), 3 decimals = thousandths (1000).
Tip 2: Always simplify fractions to their lowest terms.
Tip 3: Memorize common conversions: 0.5 = 1/2, 0.25 = 1/4, 0.75 = 3/4, 0.125 = 1/8.
Tip 4: Check your work by converting back: divide numerator by denominator.
Common errors: Forgetting to count decimal places correctly, not simplifying fractions, misplacing decimal points.
Exam preparation: Practice conversions up to thousandths, memorize common fractions, verify all answers.
Formulas to know by heart:

• Decimal places determine denominator: n places = denominator 10^n

• Simplification: Divide by GCD(numerator, denominator)

• Verification: numerator ÷ denominator should equal original decimal

Solution: Exercises 4 to 5
4 Converting Mixed Numbers
Exercise 4
Convert 2.375 to a mixed number fraction.
🎯 Goal: Express the decimal as a mixed number in simplest form.
Definition:

Mixed number: A combination of a whole number and a proper fraction (e.g., 2 3/4)

Decimal
2.375
Separate Parts
2 + 0.375
Final Answer
2 3/8
Step 1: Separate whole and decimal parts

2.375 = 2 + 0.375

Whole number part: 2

Decimal part: 0.375

Step 2: Convert decimal part to fraction

0.375 has 3 decimal places → denominator = 1000

Numerator = 375

So 0.375 = 375/1000

Step 3: Simplify the fractional part

Find GCD(375,1000): Both are divisible by 125

375÷125 = 3, 1000÷125 = 8

So 375/1000 = 3/8

Step 4: Combine whole and fractional parts

2.375 = 2 + 3/8 = 2 3/8

2.375 = 2 3/8
Final answer:

2.375 = 2 3/8

Applied rules:

• Mixed Number Conversion: Separate whole number from decimal part

• Decimal Conversion: Apply standard decimal to fraction rules to decimal part

• Simplification: Always simplify fractional part of mixed number

Tip: When converting decimals greater than 1, separate the whole number part first before converting the decimal part.
5 Converting Larger Decimals
Exercise 5
Convert 0.008 to a fraction.
🎯 Goal: Express the decimal as a fraction in simplest form.
Definition:

Thousandths: 0.008 means 8 thousandths, or 8 out of 1000 equal parts

Decimal
0.008
Initial Fraction
8/1000
Simplified
1/125
Step 1: Count decimal places

0.008 has 3 decimal places (the 8 is in the thousandths place)

Step 2: Write as fraction

Numerator = 8, Denominator = 1000 (because of 3 decimal places)

So 0.008 = 8/1000

Step 3: Simplify the fraction

Find GCD(8,1000): Factors of 8: 1,2,4,8. Factors of 1000: 1,2,4,5,8,10,20,25,40,50,100,125,200,250,500,1000

GCD(8,1000) = 8

8÷8 = 1, 1000÷8 = 125

So 8/1000 = 1/125

Step 4: Verify the result

1÷125 = 0.008 ✓

0.008 = 1/125
Final answer:

0.008 = 1/125

Applied rules:

• Decimal Place Value: Count ALL digits after decimal point, including leading zeros

• Simplification: Find the greatest common divisor to reduce fraction

• Verification: Always check by division

Tip: Leading zeros in decimals still count toward decimal places: 0.008 has 3 decimal places, not 1.
Decimal to Fraction Conversion Guide
Decimal Places → Denominator
Place Value Rule
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)

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.
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.
Key formulas: n decimal places → denominator = 10^n, then simplify by GCD.
Essential conversion rules:

• 1 decimal place: denominator = 10 (tenths)

• 2 decimal places: denominator = 100 (hundredths)

• 3 decimal places: denominator = 1000 (thousandths)

• 4 decimal places: denominator = 10000 (ten-thousandths)

• 5 decimal places: denominator = 100000 (hundred-thousandths)

Decimal to Fraction Conversion Infographic

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 Relationship

0.1 ↔ 1/10

0.25 ↔ 1/4

0.5 ↔ 1/2

0.75 ↔ 3/4

0.125 ↔ 1/8

Remember: Count decimal places, use power of 10 as denominator!

Questions & Answers

Question: I don't understand why 0.5 equals 1/2 and not 5/10. Aren't they the same thing?

Answer: Great question! You're absolutely right that 0.5 = 5/10, but we always want to write fractions in their simplest form.

Why simplify? It makes the fraction easier to work with and understand. 1/2 is simpler than 5/10 because the numbers are smaller.

How to simplify: Find the Greatest Common Divisor (GCD) of numerator and denominator:

  • Factors of 5: 1, 5
  • Factors of 10: 1, 2, 5, 10
  • GCD = 5 (largest common factor)
  • 5÷5 = 1, 10÷5 = 2
  • So 5/10 = 1/2

Both 5/10 and 1/2 represent the same amount, but 1/2 is the standard way to write it!

Question: How do I know if I should write a decimal as a mixed number or an improper fraction?

Answer: It depends on the value of the decimal:

  • If the decimal is less than 1 (like 0.7, 0.25, 0.125), convert to a proper fraction (numerator < denominator)
  • If the decimal is 1 or greater (like 1.5, 2.25, 3.75), convert to a mixed number (whole number + fraction)

Examples:

  • 0.75 = 3/4 (proper fraction)
  • 1.75 = 1 3/4 (mixed number)
  • 2.5 = 2 1/2 (mixed number)

For mixed numbers, separate the whole number part first, then convert only the decimal part to a fraction.

Question: Why does 0.008 have 3 decimal places when there are only 2 zeros before the 8?

Answer: This is a common point of confusion! When counting decimal places, we count ALL positions after the decimal point, including zeros:

  • 0.008: The first position after decimal is 0 (tenths place)
  • 0.008: The second position after decimal is 0 (hundredths place)
  • 0.008: The third position after decimal is 8 (thousandths place)

So there are 3 positions total after the decimal point, making it 3 decimal places. That's why 0.008 = 8/1000 (8 in the thousandths place).

Think of it like this: 0.008 means 8 thousandths, which is 8 out of 1000 equal parts.