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!

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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!

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Converting Fractions to Decimals

Method: Divide the numerator by the denominator

Rule: a/b = a ÷ b

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Easy Fraction to Decimal Conversions

Memorize these common fractions:

Halves:

• 1/2 = 0.5

Fourths:

• 1/4 = 0.25
• 3/4 = 0.75

Fifths:

• 1/5 = 0.2
• 2/5 = 0.4
• 3/5 = 0.6
• 4/5 = 0.8

Eighths:

• 1/8 = 0.125
• 3/8 = 0.375
• 5/8 = 0.625
• 7/8 = 0.875

Tenths:

• 1/10 = 0.1
• 3/10 = 0.3
• 7/10 = 0.7
• 9/10 = 0.9

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Step-by-Step: Fraction to Decimal

Example 1: Convert 3/8 to a decimal

Step 1: Divide numerator by denominator 3 ÷ 8 = 0.375

Answer: 3/8 = 0.375

Example 2: Convert 7/20 to a decimal

Step 1: Divide 7 ÷ 20 = 0.35

Answer: 7/20 = 0.35

Example 3: Convert 5/6 to a decimal

Step 1: Divide 5 ÷ 6 = 0.8333...

This creates a repeating decimal!

Answer: 5/6 = 0.83̄ or 0.833...

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Terminating vs Repeating Decimals

Terminating decimal:

• Ends after a finite number of digits
• Example: 1/4 = 0.25

Repeating decimal:

• Digits repeat forever in a pattern
• Example: 1/3 = 0.333... = 0.3̄

Notation for repeating:

• Bar over repeating digit(s): 0.3̄
• Three dots: 0.333...

Which fractions terminate? Fractions terminate when the denominator (in lowest terms) has ONLY factors of 2 and/or 5.

Examples:

• 1/2: Terminates (2 is a factor of 10)
• 1/5: Terminates (5 is a factor of 10)
• 1/8: Terminates (8 = 2³)
• 1/3: Repeats (3 is not a factor of 10)
• 1/6: Repeats (6 = 2×3, has factor 3)

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Converting Decimals to Fractions

Method: Use place value!

Steps:

1. Write digits as numerator
2. Write place value as denominator
3. Simplify if possible

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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

Answer: 0.6 = 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

Answer: 0.75 = 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

Answer: 0.125 = 1/8

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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

Example: 0.345

• 345 in the numerator
• Thousandths place (3 digits after decimal)
• Denominator is 1,000
• 0.345 = 345/1000 = 69/200 (simplified)

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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

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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 = 0.75
Step 3: Combine: 2 + 0.75 = 2.75

Answer: 2 3/4 = 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

Answer: 3.6 = 3 3/5

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Simplifying Fractions from Decimals

Always simplify your final answer!

Example: 0.50

0.50 = 50/100

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)

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Real-World Applications

Money:

• $0.25 = 1/4 of a dollar (quarter)
• $0.50 = 1/2 of a dollar (half dollar)
• $0.75 = 3/4 of a dollar

Measurements:

• 0.5 inches = 1/2 inch
• 2.25 pounds = 2 1/4 pounds
• 0.333 miles = about 1/3 mile

Sports:

• Batting average .250 = 1/4 (hit 1 out of 4 times)
• Free throw percentage 0.75 = 3/4

Cooking:

• 0.5 cup = 1/2 cup
• 1.25 cups = 1 1/4 cups

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Using a Calculator

To convert fraction to decimal:

• Divide numerator by denominator
• Example: 3/8 → Enter 3 ÷ 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

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Common Mistakes to Avoid

❌ Mistake 1: Wrong place value

• Wrong: 0.5 = 5/100
• Right: 0.5 = 5/10 = 1/2

❌ Mistake 2: Forgetting to simplify

• Wrong: 0.4 = 4/10 (not simplified)
• Right: 0.4 = 4/10 = 2/5

❌ Mistake 3: Misplacing decimal point

• Wrong: 3/4 = 3 ÷ 4 = 3.4
• Right: 3/4 = 3 ÷ 4 = 0.75

❌ 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

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Problem-Solving Strategy

Fraction to Decimal:

1. Divide numerator by denominator
2. Watch for terminating or repeating patterns
3. Round if asked (e.g., to nearest hundredth)

Decimal to Fraction:

1. Identify place value
2. Write as fraction
3. Simplify completely
4. Convert to mixed number if improper

Choosing which form:

• Need exact value? Use fraction
• Need to compare/compute? Use decimal
• Follow problem instructions!

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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...

Decimal Place Values:

• Tenths → /10
• Hundredths → /100
• Thousandths → /1000

Conversion Methods:

• Fraction → Decimal: Divide
• Decimal → Fraction: Use place value, simplify

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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

Tip 3: Check your work

• Convert back to verify
• 1/4 → 0.25 → 25/100 → 1/4 ✓

Tip 4: Understand the "why"

• Dividing makes sense: 1/4 means 1 divided into 4 parts
• Place value tells you the denominator

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Summary

Fraction to Decimal:

• Divide numerator by denominator
• May terminate or repeat
• Memorize common ones

Decimal to Fraction:

• Use place value for denominator
• Simplify the result
• Check that it makes sense

Both forms are useful:

• 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!