Skip to content Study Mondo Free study resources for students from Grade 4 through AP and test prep. 38 courses, 900+ topics.
Courses Features Company Stay Ahead in School Free weekly study tips, practice sets, and exam strategies. No spam, unsubscribe anytime.
ยฉ 2026 Study Mondo. Built for students.
APยฎ is a trademark registered by the College Board, which is not affiliated with, and does not endorse, this website.
Fraction and Decimal Conversions | Study Mondo
Topics / Fractions and Decimals / Fraction and Decimal Conversions Fraction and Decimal Conversions Convert between fractions and decimals
SM Written and reviewed by the Study Mondo Education Team โข Last updated April 18, 2026
๐ฏ โญ INTERACTIVE LESSON
Try the Interactive Version! Learn step-by-step with practice exercises built right in.
Start Interactive Lesson โ Fraction and Decimal Conversions
How do you switch between fractions and decimals? These two forms represent the same values but in different ways - and being able to convert between them is a fundamental math skill!
Why Convert Between Forms? Different situations call for different forms:
Fractions: Better for exact values (1/3, 2/5)Decimals: Easier to compare and compute (0.5, 0.75)Real life: Mix of both (recipes use fractions, money uses decimals) Being fluent in both gives you flexibility!
Converting Fractions to Decimals Method: Divide the numerator by the denominator
Easy Fraction to Decimal Conversions Memorize these common fractions:
1/5 = 0.2
2/5 = 0.4
3/5 = 0.6
4/5 = 0.8
1/8 = 0.125
3/8 = 0.375
5/8 = 0.625
7/8 = 0.875
1/10 = 0.1
3/10 = 0.3
7/10 = 0.7
9/10 = 0.9
Step-by-Step: Fraction to Decimal Example 1: Convert 3/8 to a decimal
Step 1: Divide numerator by denominator
3 รท 8 = 0.375
Example 2: Convert 7/20 to a decimal
Step 1: Divide
7 รท 20 = 0.35
Example 3: Convert 5/6 to a decimal
Step 1: Divide
5 รท 6 = 0.8333...
This creates a repeating decimal!
Answer: 5/6 = 0.83ฬ or 0.833...
Terminating vs Repeating Decimals
Ends after a finite number of digits
Example: 1/4 = 0.25
Digits repeat forever in a pattern
Example: 1/3 = 0.333... = 0.3ฬ
Bar over repeating digit(s): 0.3ฬ
Three dots: 0.333...
Which fractions terminate?
Fractions terminate when the denominator (in lowest terms) has ONLY factors of 2 and/or 5.
1/2: Terminates (2 is a factor of 10)
1/5: Terminates (5 is a factor of 10)
1/8: Terminates (8 = 2ยณ)
1/3: Repeats (3 is not a factor of 10)
1/6: Repeats (6 = 2ร3, has factor 3)
Converting Decimals to Fractions
Write digits as numerator
Write place value as denominator
Simplify if possible
Step-by-Step: Decimal to Fraction Example 1: Convert 0.6 to a fraction
Step 1: 6 is in tenths place
0.6 = 6/10
Step 2: Simplify
6/10 = 3/5
Example 2: Convert 0.75 to a fraction
Step 1: 75 is in hundredths place
0.75 = 75/100
Step 2: Simplify
75/100 = 3/4
Example 3: Convert 0.125 to a fraction
Step 1: 125 is in thousandths place
0.125 = 125/1000
Step 2: Simplify
125/1000 = 1/8
Place Value Review Decimal places and denominators:
Tenths (0.#): denominator is 10
Hundredths (0.##): denominator is 100
Thousandths (0.###): denominator is 1,000
Ten-thousandths (0.####): denominator is 10,000
345 in the numerator
Thousandths place (3 digits after decimal)
Denominator is 1,000
0.345 = 345/1000 = 69/200 (simplified)
Converting Repeating Decimals For simple repeating decimals like 0.333...:
Shortcut: Know common patterns
0.333... = 1/3
0.666... = 2/3
0.111... = 1/9
0.222... = 2/9
For other repeating decimals, use algebra (advanced):
Example: 0.454545... = 45/99 = 5/11
Mixed Numbers and Decimals Converting mixed numbers to decimals:
Example: 2 3/4 to decimal
Step 1: Keep whole number: 2
Step 2: Convert fraction: 3/4 = 0.75Step 3: Combine: 2 + 0.75 = 2.75
Converting decimals to mixed numbers:
Example: 3.6 to mixed number
Step 1: Whole number is 3
Step 2: Decimal part: 0.6 = 6/10 = 3/5
Step 3: Combine: 3 3/5
Simplifying Fractions from Decimals Always simplify your final answer!
Simplify by dividing both by 50:
50/100 = 1/2
Shortcuts for simplifying:
Both even? Divide by 2
End in 0 or 5? Divide by 5
Find GCF (Greatest Common Factor)
Real-World Applications
$0.25 = 1/4 of a dollar (quarter)
$0.50 = 1/2 of a dollar (half dollar)
$0.75 = 3/4 of a dollar
0.5 inches = 1/2 inch
2.25 pounds = 2 1/4 pounds
0.333 miles = about 1/3 mile
Batting average .250 = 1/4 (hit 1 out of 4 times)
Free throw percentage 0.75 = 3/4
0.5 cup = 1/2 cup
1.25 cups = 1 1/4 cups
Using a Calculator To convert fraction to decimal:
Divide numerator by denominator
Example: 3/8 โ Enter 3 รท 8 = 0.375
To convert decimal to fraction:
Calculator won't do this automatically!
Use place value method by hand
Or use online converters for complex decimals
Common Mistakes to Avoid โ Mistake 1: Wrong place value
Wrong: 0.5 = 5/100
Right: 0.5 = 5/10 = 1/2
โ Mistake 2: Forgetting to simplify
Wrong: 0.4 = 4/10 (not simplified)
Right: 0.4 = 4/10 = 2/5
โ Mistake 3: Misplacing decimal point
Wrong: 3/4 = 3 รท 4 = 3.4
Right: 3/4 = 3 รท 4 = 0.75
โ Mistake 4: Treating whole and decimal separately
Wrong: 2.5 = 2 and 5/10 kept separate
Right: 2.5 = 2 5/10 = 2 1/2
Problem-Solving Strategy
Divide numerator by denominator
Watch for terminating or repeating patterns
Round if asked (e.g., to nearest hundredth)
Identify place value
Write as fraction
Simplify completely
Convert to mixed number if improper
Need exact value? Use fraction
Need to compare/compute? Use decimal
Follow problem instructions!
Quick Reference Common Fractions to Decimals:
1/2 = 0.5
1/4 = 0.25, 3/4 = 0.75
1/5 = 0.2, 2/5 = 0.4, 3/5 = 0.6, 4/5 = 0.8
1/8 = 0.125
1/3 = 0.333...
Tenths โ /10
Hundredths โ /100
Thousandths โ /1000
Fraction โ Decimal: Divide
Decimal โ Fraction: Use place value, simplify
Practice Tips Tip 1: Memorize common conversions
Saves time and builds fluency
Focus on halves, fourths, fifths, eighths
Tip 2: Always simplify fractions
Makes answers cleaner
Easier to recognize equivalent forms
Convert back to verify
1/4 โ 0.25 โ 25/100 โ 1/4 โ
Tip 4: Understand the "why"
Dividing makes sense: 1/4 means 1 divided into 4 parts
Place value tells you the denominator
Summary
Divide numerator by denominator
May terminate or repeat
Memorize common ones
Use place value for denominator
Simplify the result
Check that it makes sense
Fractions show exact relationships
Decimals are easier to compare
Being fluent in both is essential!
Mastering conversions between fractions and decimals unlocks flexibility in solving all kinds of math problems!
๐ Practice Problems
1 Problem 1easy โ Question:Convert 3/4 to a decimal.
๐ก Show Solution Method: Divide numerator by denominator.
3 รท 4 = ?
Set up division:
0.75
4)3.00
-28
20
-20
0
Answer: 3/4 = 0.75
This is a terminating decimal (ends).
2 Problem 2easy โ Question:Convert 0.6 to a fraction in simplest form.
๐ก Show Solution Step 1: Use place value.
0.6 = 6 tenths = 6/10
Step 2: Simplify.
Find GCF of 6 and 10 = 2
6/10 = (6รท2)/(10รท2) = 3/5
Answer: 0.6 = 3/5
3 Problem 3medium โ Question:Convert 5/8 to a decimal.
๐ก Show Solution Divide: 5 รท 8
0.625
8)5.000
-48
20
-16
40
-40
0
Answer: 5/8 = 0.625
This is a terminating decimal.
4 Problem 4medium โ Question:Convert 0.35 to a fraction in simplest form.
๐ก Show Solution Step 1: Use place value.
0.35 = 35 hundredths = 35/100
Step 2: Simplify.
Find GCF of 35 and 100 = 5
35/100 = (35รท5)/(100รท5) = 7/20
Check: Can 7/20 be simplified further?
7 is prime, doesn't divide 20.
Already in simplest form.
Answer: 0.35 = 7/20
5 Problem 5hard โ Question:A recipe calls for 2.75 cups of flour. Express this as a mixed number in simplest form.
๐ก Show Solution Step 1: Separate whole and decimal parts.
2.75 = 2 + 0.75
Step 2: Convert decimal part to fraction.
0.75 = 75 hundredths = 75/100
Step 3: Simplify the fraction.
GCF of 75 and 100 = 25
75/100 = (75รท25)/(100รท25) = 3/4
Step 4: Write as mixed number.
2 + 3/4 = 2 3/4
Answer: 2.75 = 2 3/4 cups
Note: 3/4 cup is a common measurement in cooking!
Explain using: ๐ Simple words ๐ Analogy ๐จ Visual desc. ๐ Example ๐ก Explain
โ ๏ธ Common Mistakes: Fraction and Decimal ConversionsAvoid these 3 frequent errors
1 Distributing exponents over addition: (a+b)ยฒ โ aยฒ+bยฒ
โพ 2 Canceling terms instead of factors
โพ 3 Forgetting to flip the inequality sign when multiplying/dividing by a negative
โพ ๐ Real-World Applications: Fraction and Decimal ConversionsSee how this math is used in the real world
๐ฐ Budgeting & Finance
Finance
โพ ๐ป Game Development
Technology
โพ ๐๏ธ Architecture & Design
Architecture
โพ
๐ Worked Example: Solving a Quadratic by FactoringProblem: Solve x 2 โ 5 x + 6 = 0 x^2 - 5x + 6 = 0 x 2 โ 5 x + 6 = 0
1 Look for two numbers that multiply to 6 and add to -5 Click to reveal โ
3 Set each factor equal to zero
๐งช Practice Lab Interactive practice problems for Fraction and Decimal Conversions
โพ ๐ Related Topics in Fractions and Decimalsโ Frequently Asked QuestionsWhat is Fraction and Decimal Conversions?โพ Convert between fractions and decimals
How can I study Fraction and Decimal Conversions effectively?โพ Start by reading the study notes and working through the examples on this page. Then use the flashcards to test your recall. Practice with the 5 problems provided, checking solutions as you go. Regular review and active practice are key to retention.
Is this Fraction and Decimal Conversions study guide free?โพ Yes โ all study notes, flashcards, and practice problems for Fraction and Decimal Conversions on Study Mondo are free to access. No account is needed.
What course covers Fraction and Decimal Conversions?โพ Fraction and Decimal Conversions is part of the Pre-Algebra course on Study Mondo, specifically in the Fractions and Decimals section. You can explore the full course for more related topics and practice resources.
Are there practice problems for Fraction and Decimal Conversions?โพ Yes, this page includes 5 practice problems with detailed solutions. Each problem includes a step-by-step explanation to help you understand the approach.
๐ก Study Tipsโ Work through examples step-by-step โ Practice with flashcards daily โ Review common mistakes