How do you convert any fraction into a decimal?

Divide the numerator (top number) by the denominator (bottom number) using long division or a calculator: 3/4 = 3 ÷ 4 = 0.75.

How do you convert a decimal into a percentage?

Multiply the decimal by 100 (which is the same as moving the decimal point two places to the right) and add the "%" symbol: 0.85 × 100 = 85%, and 0.04 × 100 = 4%.

How do you convert a percentage into a fraction in simplest terms?

Remove the "%" sign, put the number over 100, and simplify by finding the Greatest Common Divisor (GCD): 75% = 75/100 = 3/4.

What are the most common benchmark conversions students should memorize?

1/2 = 0.5 = 50%, 1/4 = 0.25 = 25%, 3/4 = 0.75 = 75%, 1/5 = 0.2 = 20%, 1/10 = 0.1 = 10%, 1/8 = 0.125 = 12.5%, and 1/3 ≈ 0.333 = 33.3%.

Why is 0.05 not equal to 50%?

Moving the decimal two places to the right on 0.05 gives 5%, not 50%! 50% is 0.50 (five tenths). Always be careful with single-digit percentage zeros: 0.01 = 1%, 0.05 = 5%, 0.50 = 50%.

fractions

Fractions, Decimals & Percents (The Conversion Triangle)

January 18, 2026

6 min read

PanMaths Team

⚡ THE 3 CONVERSION RULES

Frac ➔ Dec: N ÷ D 

 Dec ➔ %: × 100 

 % ➔ Frac: P / 100

1. Fraction to Decimal: Divide top by bottom ➔ 2. Decimal to Percent: Move decimal 2 places right (× 100) ➔ 3. Percent to Fraction: Put over 100 and simplify

📐 Fractions & Decimals Masterclass • Upper Elementary & Middle School (Grades 4–7)

Fractions, Decimals & Percents: The Rosetta Stone Conversion Triangle

🔬 Try 3-Way Slicer 👇

💡 STEP 1: THE INTUITION

The 3 Languages of Math: Fractions, Decimals & Percentages

🏛️ THE MATHEMATICAL ROSETTA STONE

Universal Decoder

1. Slices (Fractions)

3/4

Pizza slices & ratio parts

2. Metric (Decimals)

0.75

Calculators & measurements

3. Commerce (Percents)

75%

Discounts & parts per hundred

📜 The Historical Analogy: In 1799, the Rosetta Stone unlocked ancient Egyptian hieroglyphs by writing the same decree in 3 languages. In math, 3/4, 0.75, and 75% are the exact same value—just written in 3 different dialects!

📜 STEP 2: THE 6 CONVERSION PATHWAYS

The 6-Way Conversion Blueprint

1. Fraction ➔ Decimal

Numerator ÷ Denominator

Divide top by bottom: 3/4 = 3 ÷ 4 = 0.75.

2. Decimal ➔ Percent

Decimal × 100 (Shift Right 2)

Move decimal 2 spots right: 0.75 ➔ 75%.

3. Percent ➔ Decimal

Percent ÷ 100 (Shift Left 2)

Remove % and shift 2 spots left: 85% ➔ 0.85.

4. Percent ➔ Fraction

Percent / 100 & Simplify

75% = 75/100. Divide by 25 = 3/4.

🔬 INTERACTIVE CONVERSION TRIANGLE

Live 3-Way Conversion Simulator

Select any benchmark fraction to see how it automatically renders in all 3 mathematical dialects:

Benchmark: 1/2 = 0.5 = 50% (The Half Benchmark)Half

🍰 Fraction Dialect

1/2

1 out of 2 parts

🧮 Decimal Dialect

0.5

Base-10 Metric Value

📈 Percent Dialect

50%

Parts Per Hundred

1. Fraction ➔ Decimal

➗ 1 ÷ 2 = 0.5

Divide numerator (1) by denominator (2) = 0.5.

⚠️ EXAM MISTAKE RADAR

3 Mistakes Students Make on Conversion Exams

1. The Decimal Shift Zero Error

Writing 0.05 = 50%. Moving 2 places right gives 5%! 50% is 0.50. Always be careful with single-digit percent zeros.

2. The "Dot Shortcut" Error

Writing 3/8 = 3.8. You cannot simply insert a decimal point! You must divide: 3 ÷ 8 = 0.375.

3. Forgetting to Simplify the Converted Fraction

Leaving 0.6 = 6/10. Always reduce to simplest terms: 6/10 = 3/5!

🧠 ACTIVE RECALL QUIZ

Test Your Understanding in 60 Seconds

Select your answers and click "Check Answers" to test your mastery:

Question 1: What is 3/5 written as a percentage?

Question 2: What is 0.05 converted to a percentage?

Question 3: What is 80% expressed as a fraction in simplest terms?

🎓 Practice & Mastery Funnel

Print Decimal & Fraction Worksheets

Generate 20 customizable practice problems for converting fractions, decimals, and percents with instant PDF answer keys.

🖨️ Print Free Worksheet →

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Custom Math Quiz & Test Maker

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✓Anti-cheat Set A & Set B with alternate numbers for adjacent desks
✓100% step-by-step teacher grading keys with intermediate lines
✓1-click Google Classroom links for student tablet/Chromebook testing

✨ Build Custom Worksheet in 15 Seconds →

🎓 100% Free for Teachers & Parents • No Signups Required • Pure Printable PDF

PANMATHS.COM • CONVERSION CHEAT SHEET

Fractions, Decimals & Percents Benchmark Chart (Grades 4–7)

Name: _______________________________

Date: _______________ Period: ________

1. FRACTION ➔ DECIMAL

Numerator ÷ Denominator

3/4 = 3 ÷ 4 = 0.75

2. DECIMAL ➔ PERCENT

Decimal × 100 (Shift 2 Right)

0.75 × 100 = 75%

3. PERCENT ➔ FRACTION

Percent / 100 & Simplify

75% = 75/100 = 3/4

Benchmark Family	Fraction	Decimal	Percentage
Halves	1/2	0.5	50%
Quarters	1/4, 3/4	0.25, 0.75	25%, 75%
Fifths	1/5, 2/5, 3/5, 4/5	0.2, 0.4, 0.6, 0.8	20%, 40%, 60%, 80%
Eighths	1/8, 3/8, 5/8, 7/8	0.125, 0.375, 0.625, 0.875	12.5%, 37.5%, 62.5%, 87.5%
Thirds	1/3, 2/3	0.333..., 0.666...	33.3%, 66.7%

🚫 THE 0.05 VS 50% TRAP

0.05 = 5%! (0.50 = 50%). Move the decimal point exactly two spots right.

🔄 NEVER JUST ADD A DOT

3/8 ≠ 3.8! Always divide top by bottom (3 ÷ 8 = 0.375).

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✨ Free Classroom Assessment ToolSet A & Set B Anti-Cheat

Custom Math Quiz & Test Maker

Need a mixed Friday review or unit assessment? Create a custom test combining multiple math skills in 15 seconds.

✓Anti-cheat Set A & Set B with alternate numbers for adjacent desks
✓100% step-by-step teacher grading keys with intermediate lines
✓1-click Google Classroom links for student tablet/Chromebook testing

✨ Build Custom Worksheet in 15 Seconds →

🎓 100% Free for Teachers & Parents • No Signups Required • Pure Printable PDF

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📚 Related Topics

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Fractions

Fractions, Decimals & Percents (The Conversion Triangle)

Fractions, Decimals & Percents: The Rosetta Stone Conversion Triangle

The 3 Languages of Math: Fractions, Decimals & Percentages

The 6-Way Conversion Blueprint

Live 3-Way Conversion Simulator

3 Mistakes Students Make on Conversion Exams

Test Your Understanding in 60 Seconds

Print Decimal & Fraction Worksheets

Custom Math Quiz & Test Maker

Need Practice Worksheets for This Topic?

Custom Math Quiz & Test Maker

Help us make PanMaths even better for your classroom!

Need to Calculate?

📚 Related Topics

Mixed Numbers & Improper Fractions

Repeating Decimals to Fractions

Adding Fractions with Unlike Denominators

Percentage Increase and Decrease