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Ratio Calculator

Simplify ratios to their lowest terms, scale them up or down, and convert to decimals and percentages so you can compare ratios numerically. Free math tool for students, cooks, and professionals.

Last revised 2 September 2026

By Team GlobalCalqulate · About our editorial standards

Ratio Input

Value A

Value B

Operation

Scale Factor

For scaling operations.

Decimal Places

Simplified Ratio

2:3

Original: 10:15

Methodology

Formula:: Simplify a ratio
Content last updated:: September 2026
Scheduled re-verification:: September 2027

Calculation type: Exact calculation.

Formula & methodology

Formula used

Simplify a ratio

A : B → (A ÷ g) : (B ÷ g),  where g = greatest common divisor of A and B

Both sides are divided by their greatest common divisor to give the ratio in its lowest terms.

Ratio as a decimal or percentage

decimal = A ÷ B;  percentage = (A ÷ B) × 100

Every ratio operation divides by B, which is why B cannot be zero.

Scale a ratio

A : B → (A × k) : (B × k)

Multiplying both sides by the same factor preserves the ratio.

Variable definitions

Symbol	Meaning	Unit
A	First term. the left-hand side of the ratio	—
B	Second term. the right-hand side; cannot be zero	—
k	Scale factor. the factor both sides are multiplied by	—

Step-by-step calculation

1. Enter both terms
B must be non-zero, since every operation divides by it.
2. Choose the operation
Simplify, convert to decimal or percentage, or scale by a factor.

Limitations

A ratio and a fraction of the whole are different things. A ratio of 1 : 3 means one part in four, not one third — a common source of error in mixing and dilution.
Simplification to lowest terms uses the greatest common divisor, which is exact for whole numbers; decimal inputs are handled numerically and may round.

This page is educational. It applies the formula described above to the figures you enter and shows the arithmetic behind the result. The output is only as good as the inputs and the assumptions listed here, and it is general information rather than advice about your particular situation.

Help & FAQs

Frequently Asked Questions

Clear answers to common questions to help you use this calculator confidently.

What is a ratio and how do I simplify it?

Tap to view the answer

A ratio expresses the relationship between two quantities (e.g., 2:3). To simplify, divide both numbers by their greatest common divisor (GCD). For example, 12:18 simplifies to 2:3 by dividing both by 6. This calculator does this automatically using the GCD algorithm.

How do I convert a ratio to a decimal or percentage?

Tap to view the answer

To convert a ratio to a decimal, divide the first number by the second (e.g., 3:4 = 3÷4 = 0.75). To convert to a percentage, multiply the decimal by 100% (0.75 × 100% = 75%) — meaning the first value is 75% of the second value.

What does it mean to scale a ratio?

Tap to view the answer

Scaling means multiplying both numbers by the same factor to proportionally increase or decrease the ratio. For example, scaling 2:3 by 5 gives 10:15. The relationship stays the same, but the quantities change — essential for scaling recipes, blueprints, and designs.

What's the difference between a ratio and a proportion?

Tap to view the answer

A ratio (2:3) compares two quantities. A proportion is an equation stating two ratios are equal (2:3 = 4:6). Ratios describe relationships, while proportions solve for unknown values — use this calculator for simplifying ratios, and a proportion calculator to find missing values.

How do I check if two ratios are equivalent?

Tap to view the answer

Use cross multiplication: if a:b and c:d are equivalent, then a×d = b×c. Example: is 2:3 equivalent to 4:6? Check: 2×6 = 12 and 3×4 = 12 — they match, so yes, the ratios are equivalent.

Need more help? Contact support or email globalcalqulate@gmail.com

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How to Use This Calculator

Enter Two Values

Input the two numbers forming your ratio (A:B). For example, 10 and 15 for the ratio 10:15.

Choose an Operation

Simplify reduces to lowest terms (10:15 → 2:3). Scale multiplies both terms by a factor. Convert shows as decimal or percentage.

Review Results

See the simplified or scaled ratio, decimal value (A÷B), and percentage (A÷B×100).

Understanding Your Results

Ratio
A comparison of two quantities: A:B. 10:15 means for every 10 of A, there are 15 of B. Equivalent to the fraction 10/15.
Simplification
Divide both terms by their greatest common divisor (GCD). 10:15 → GCD=5 → 2:3. Both ratios represent the same proportion.
Scaling
Multiply both terms by the same number to find an equivalent ratio. 2:3 scaled by 5 = 10:15. Useful for recipes, maps, and blueprints.

Key Tips

✓
A ratio A:B is the same as the fraction A/B. Simplify by finding the GCD of A and B.
✓
Scaling ratios is essential for recipes: if the recipe ratio is 2 cups flour to 1 cup sugar (2:1), scaling by 3 gives 6 cups flour and 3 cups sugar.
✓
Decimal and percentage conversions let you compare ratios numerically: 3:4 = 0.75 = 75%, while 5:8 = 0.625 = 62.5%.
✓
Ratios are used everywhere: finance (debt-to-equity), cooking, maps, screen resolutions (16:9), and photo aspect ratios.

How Ratios Work

What Is a Ratio?

A ratio compares two quantities by division. Written as A:B or 'A to B,' it tells you how many parts of A there are for each part of B. In a classroom with 10 boys and 15 girls, the ratio of boys to girls is 10:15, which simplifies to 2:3. This means for every 2 boys there are 3 girls. Ratios are the foundation of proportions, rates, and many real-world calculations.

Simplifying and Scaling Ratios

Simplifying uses the greatest common divisor (GCD) — the largest number that divides both terms evenly. For 10:15, GCD=5, giving 2:3. Scaling is the reverse: multiply both terms by the same factor. If a recipe calls for a 3:2 ratio of flour to sugar and you need 3 times the recipe, scale by 3 to get 9:6. The ratio itself (3:2=1.5, 9:6=1.5) stays the same — only the quantities change.

Comparing Ratios Using Decimals and Percentages

To compare two ratios, convert each to a decimal by dividing A by B. 3:4 = 0.75 (75%), 5:8 = 0.625 (62.5%). The higher the ratio as a percentage, the larger A is relative to B. This is useful when deciding which product offers better value (price-to-quantity ratio), which investment has a better return-to-risk ratio, or which candidate won by a larger margin.

Mistake 1: Confusing Ratio Order (a:b vs b:a

The Problem: 2:3 is NOT the same as 3:2. Reversing the order changes the entire meaning and calculation results. Example:. • 2:3 = 0.6667 (decimal) = 66.67% (percentage). • 3:2 = 1.5 (decimal) = 150% (percentage). Solution: Always maintain consistency. If your recipe calls for a 2:3 oil-to-vinegar ratio, keep that order. Reversing it creates a completely different proportion.

Mistake 2: Using Zero or Negative Numbers

The Problem: Ratios require positive numbers. Zero or negative values create undefined or meaningless results. Division by zero is mathematically impossible. Invalid Examples:. • 5:0 (division by zero—undefined). • -3:4 (negative values don't apply to most ratios). • 0:0 (completely undefined). Solution: Always use positive, non-zero numbers. Check your input values before calculating to ensure both numbers are greater than zero.

Mistake 3: Forgetting to Simplify Ratios

The Problem: Presenting ratios like 50:75 instead of 2:3 is confusing and harder to work with. Simplified ratios are clearer and more professional. Example:. • Unsimplified: 50:75 (harder to understand). • Simplified: 2:3 (clearer and more useful). Solution: Always simplify to lowest terms using GCD. Our calculator does this automatically, but when working manually, divide both numbers by their greatest common divisor.

Mistake 4: Miscalculating Scale Factors

The Problem: Applying incorrect scale factors leads to wrong quantities when scaling recipes, blueprints, or designs. A 2× scale should double BOTH numbers, not just one. Example of Error:. • Original Ratio: 2:3. • Scale Factor: 2. • Wrong: 4:3 (only scaled first number). • Correct: 4:6 (scaled both numbers). Solution: Multiply BOTH terms by the same scale factor. The relationship 2:3 must maintain when scaled, so 2×2: 3×2 = 4:6.

Mistake 5: Mixing Different Units Without Conversion

The Problem: Comparing 12 inches to 2 feet without converting units first creates invalid ratios. Always ensure both numbers use the same unit of measurement. Example of Error:. • Wrong: 12 inches: 2 feet = 12:2 (mixed units). • Correct: 12 inches: 24 inches = 12:24 = 1:2. Solution: Convert all measurements to the same unit before entering them into the calculator. For architectural drawings, use feet-to-feet or inches-to-inches, never mixed units.

Mistake 6: Not Understanding Decimal & Percentage Conversions

The Problem: Misinterpreting decimal or percentage values leads to incorrect conclusions about ratio relationships. A 0.75 decimal doesn't mean 75% in some contexts. Correct Interpretation:. • 3:4 ratio → 0.75 decimal → 75% percentage. • Meaning: First value is 75% of second value. • Not: 25% of the total (this is a different context). Solution: Remember: decimal = first ÷ second. A 0.75 decimal means the first number is 75% of the second number, not 75% of a whole.

Mistake 7: Ignoring Rounding Errors in Manual Calculations

The Problem: Manual ratio calculations often involve rounding, which compounds errors across multiple steps. What seems like a 2:3 ratio might actually be 2.001:3.002 after rounding. Example:. • Manual calculation: 10 ÷ 15 = 0.6667 (rounded). • Simplified ratio: 10:15 = 2:3. Solution: Use our online ratio calculator to avoid rounding errors. It provides exact results without manual computation mistakes. For critical applications (architecture, finance), precision matters.

Mistake 8: Applying Recipe Ratios to Non-Proportional Elements

The Problem: Not all ingredients scale linearly. Spices, salt, and seasonings may need different scaling than wet ingredients. A 2:3 ratio doesn't automatically apply to all recipe components. Example:. • Scales well: Oil:Vinegar = 2:3 (double recipe = 4:6). • Doesn't scale linearly: Salt, pepper, garlic (double recipe ≠ 2× seasoning). Solution: Use the calculator for base ingredients that scale linearly. For seasonings and spices, adjust by taste. Professional chefs know that flavor compounds don't follow simple ratio scaling.

Ratio Calculator Best Practices Checklist

Always use positive, non-zero numbers Maintain consistent order (a:b stays a:b) Ensure both numbers use the same unit Always simplify to lowest terms Scale both terms equally (same factor) Understand decimal & percentage conversions Use tools to avoid rounding errors Verify results make sense in context.

What is a Ratio Calculator?

A ratio calculator is a powerful mathematical tool that simplifies, scales, and compares ratios instantly. Whether you're working with recipes, construction blueprints, financial ratios, or academic problems, this calculator eliminates manual calculation errors and saves valuable time. Instead of laboriously finding the greatest common divisor (GCD) by hand, our tool processes any ratio and returns the simplified form, decimal equivalent, and percentage conversion in seconds. Ratios are fundamental mathematical concepts used across countless disciplines. They express the relationship between two quantities, making them essential for scaling proportions, comparing values, and solving real-world problems. A ratio calculator transforms complex ratio mathematics into an intuitive, visual experience—making advanced calculations accessible to everyone from students to professionals.

Why Ratios Matter

• Recipe Scaling: Double or triple a recipe by scaling ingredient ratios proportionally. • Construction & Design: Maintain aspect ratios for blueprints, floor plans, and architectural drawings. • Financial Analysis: Compare company metrics using debt-to-equity, price-to-earnings, and other financial ratios. • Student Success: Solve algebra problems, geometry assignments, and math tests involving ratio proportions. • Photography & Video: Maintain correct aspect ratios (16:9, 4:3, 1:1) across all media formats.

Real-World Applications of Ratio Calculators

Cooking & Baking: Professional chefs and home cooks use ratio calculators to scale recipes. If a sauce calls for a 2:3 ratio of oil to vinegar and you need to make 5 times the amount, the calculator instantly shows 10:15, which simplifies to 2:3—ensuring perfect flavor proportions every time. Business & Finance: Financial analysts rely on ratio calculators to analyze company performance. The debt-to-equity ratio, current ratio, and quick ratio are critical for investment decisions. This calculator converts complex financial data into understandable proportions in real-time. Construction & Architecture: Architects and contractors must maintain precise aspect ratios for designs. Whether scaling a 1:50 model to a 1:100 blueprint, the ratio calculator ensures measurements stay proportional across all project stages. Education & Tutoring: Students use ratio calculators to verify homework answers, understand ratio concepts, and prepare for standardized tests (SAT, ACT, GMAT) where ratio problems frequently appear. Photography & Digital Media: Content creators scale images while maintaining aspect ratios. An 8:5 ratio (landscape) might need to fit a 16:9 social media format—the calculator helps professionals make informed aspect ratio decisions. Supply Chain & Inventory: Logistics managers track supplier ratios, stock-to-sales ratios, and material proportions. Ratio calculators help optimize inventory management and procurement decisions.

Key Benefits of Using Our Ratio Calculator

• Lightning-fast calculations: Get results instantly with no delays. • Multiple formats: View ratios as simplified, decimal, and percentage forms simultaneously. • Scaling capability: Scale any ratio by any factor for real-world applications. • Beginner-friendly: No mathematical expertise required—just enter numbers and get results. • Precise: Eliminates human error in manual ratio calculations. • Free forever: No subscriptions, no hidden fees, unlimited calculations.

Example 1: Photography Aspect Ratio Conversion

Scenario:. A photographer is converting images from traditional 4:3 aspect ratio to modern 16:9 widescreen format. Input:. • First Number: 4. • Second Number: 3. Calculator Results:. • Simplified Ratio: 4:3 (already simplified). • Decimal: 1.3333 (width is 1.33× height). • Percentage: 133.33% (width is 133.33% of height). Real-World Application:. A 1200×900 pixel image maintains 4:3 aspect ratio. To convert to 16:9, you'd scale by factor 1.333, resulting in 1600×900 pixels for proper widescreen display.

Example 2: Recipe Ingredient Ratio Scaling

Scenario:. A chef needs to scale a pasta sauce recipe from 2 parts tomato to 5 parts cream, but wants to make 10 servings instead of 2. Input:. • First Number: 2. • Second Number: 5. Calculator Results:. • Simplified Ratio: 2:5 (already simplified). • Decimal: 0.4000 (tomato is 40% of cream volume). • Percentage: 40.00%. Scaling for 5× Recipe:. • Scale Factor: 5. • Scaled Ratio: 10:25. • Interpretation: Use 10 cups tomato + 25 cups cream. Result:. Perfect sauce consistency is maintained at any scale because the 2:5 ratio is preserved—the result is both more efficient and consistent in taste.

Example 3: Debt-to-Equity Financial Ratio

Scenario:. An investor is analyzing a company with $150 million in debt and $250 million in equity to assess financial health. Input:. • First Number: 150 (debt). • Second Number: 250 (equity). Calculator Results:. • Simplified Ratio: 3:5 (simplified from 150:250). • Decimal: 0.6000 (debt-to-equity ratio). • Percentage: 60.00% (debt is 60% of equity). Investment Insight:. A 0.6 debt-to-equity ratio (or 3:5) is considered healthy for most industries. The company has $3 in debt for every $5 in equity, indicating moderate financial leverage and manageable risk.

Example 4: Architectural Blueprint Scaling

Scenario:. An architect drew a model at 1:50 scale (1 unit on drawing = 50 units in reality) but needs to convert it to 1:100 scale for the final blueprint. Input:. • First Number: 1. • Second Number: 50. Calculator Results:. • Simplified Ratio: 1:50 (already simplified). • Decimal: 0.0200 (2% of real-world size). • Percentage: 2.00%. Scaling Action:. • Scale Factor: 2 (to convert 1:50 to 1:100). • Scaled Ratio: 2:100. • Interpretation: New drawing must be half the size to maintain 1:100 scale. Result:. All architectural elements maintain proper proportions at the new scale—doors, windows, walls, and structural elements scale uniformly for accurate construction planning.

Fundamental Ratio Formula

Ratio = a: b (read as "a to b"). Where a is the first term and b is the second term. Ratio Representations: • As Ratio: 2:3. • As Fraction: 2/3. • As Decimal: 0.6667 (decimal = a ÷ b). • As Percentage: 66.67% (percentage = decimal × 100%).

Simplifying Ratios Using GCD

To simplify a ratio, divide both numbers by their Greatest Common Divisor (GCD). The GCD is the largest number that divides both values evenly. Formula:. Simplified Ratio = (a ÷ GCD): (b ÷ GCD). Example:. • Original Ratio: 18:24. • GCD of 18 and 24: 6. • Simplified: (18÷6): (24÷6) = 3:4. Why simplify? Simplified ratios are easier to understand and work with. The ratios 18:24 and 3:4 represent the same relationship, but 3:4 is clearer and more useful for calculations.

Scaling Ratios by a Factor

To scale a ratio proportionally, multiply both numbers by the same scaling factor. This maintains the relationship between the two values. Formula:. Scaled Ratio = (a × scale): (b × scale). Example:. • Original Ratio: 2:3. • Scale Factor: 5. • Scaled Ratio: (2×5): (3×5) = 10:15. Key Principle: The relationship between numbers stays the same. 2:3 = 10:15 = 20:30 = 100:150. All represent the same proportion.

Converting Ratios to Decimals & Percentages

Decimal Conversion: Decimal = First Number ÷ Second Number. Example: 3:4 = 3 ÷ 4 = 0.75. Percentage Conversion: Percentage = (First Number ÷ Second Number) × 100%. Example: 3:4 = (3 ÷ 4) × 100% = 75%. Common Ratio Conversions:. • 1:1 = 1.0 = 100%. • 1:2 = 0.5 = 50%. • 1:3 = 0.3333 = 33.33%. • 1:4 = 0.25 = 25%. • 2:3 = 0.6667 = 66.67%. • 3:4 = 0.75 = 75%. • 16:9 = 1.7778 = 177.78%. • 4:3 = 1.3333 = 133.33%.

Finding Equivalent Ratios

Equivalent ratios are ratios that represent the same relationship but use different numbers. They're created by multiplying (or dividing) both terms by the same value. Example:. Original Ratio: 2:3. Equivalent Ratios:. • 2:3 = 4:6 (multiply by 2). • 2:3 = 6:9 (multiply by 3). • 2:3 = 10:15 (multiply by 5). • 2:3 = 20:30 (multiply by 10). Practical Use: When scaling recipes, blueprints, or designs, you create equivalent ratios. A 2:3 ingredient ratio is equivalent to 10:15 or 20:30—you're using the same proportions, just different quantities.

Key Mathematical Principles

1. Proportionality Principle. If a:b = c:d, then a×d = b×c. This relationship helps solve missing values in proportions. 2. Commutativity. The order matters—a:b ≠ b:a. A 2:3 ratio is different from a 3:2 ratio (inverse relationship). 3. Scale Invariance. Scaling both numbers by the same factor preserves the ratio. 2:3 = 20:30 because the relationship is unchanged. 4. Simplification. Every ratio can be simplified to lowest terms by dividing by the GCD. This creates the most basic form of the ratio. 5. Cross Multiplication. For ratios a:b and c:d, if a:b = c:d, then a×d = b×c. Used to find missing values in proportions.

Step-by-Step Guide

1. Enter Your First Number Type the first number of your ratio in the input field. This represents the left side of the ratio (the numerator or first term). 2. Enter Your Second Number Type the second number of your ratio in the second input field. This represents the right side of the ratio (the denominator or second term). The calculator instantly displays simplified results. 3. View the Simplified Ratio The calculator automatically simplifies your ratio to its lowest terms using the greatest common divisor (GCD) method. For example, 15:20 becomes 3:4. 4. Check Decimal & Percentage Conversions See your ratio expressed as a decimal and percentage. The 3:4 ratio equals 0.75 as a decimal or 75% as a percentage—useful for different applications. 5. Scale Your Ratio (Optional) Enter a scale factor to multiply your original ratio. If you need to scale 3:4 by 5, the calculator returns 15:20, helping you proportionally increase recipes, designs, or measurements.

Real-World Example: Scaling a Recipe

Scenario: You're making a salad dressing with a 2:3 oil-to-vinegar ratio, but you need triple the quantity for a dinner party. Input:. First Number: 2 | Second Number: 3. Calculator Results:. • Simplified Ratio: 2:3 (already in simplest form). • Decimal: 0.6667 (meaning oil is 66.67% of vinegar volume). • Percentage: 66.67% (useful for recipe scaling). Scaling for 3× yield: Enter scale factor 3. • Scaled Ratio: 6:9. • Interpretation: Use 6 tablespoons of oil and 9 tablespoons of vinegar. Final Result: Your perfectly proportioned dressing is ready for the party!.

Pro Tip: Common Ratio Patterns

Understanding common ratio patterns helps you use this calculator more effectively:. • 1:1 ratios (equal parts) = 1.0 decimal = 100% - use for mixing equal quantities. • 1:2 ratios (one-to-double) = 0.5 decimal = 50% - common in recipes. • 2:3 ratios = 0.667 decimal = 66.7% - standard for many formulas. • 16:9 ratios = 1.778 decimal = 177.8% - standard widescreen aspect ratio.

Formula & methodology

Formula used

Simplify a ratio

A : B → (A ÷ g) : (B ÷ g),  where g = greatest common divisor of A and B

Both sides are divided by their greatest common divisor to give the ratio in its lowest terms.

Ratio as a decimal or percentage

decimal = A ÷ B;  percentage = (A ÷ B) × 100

Every ratio operation divides by B, which is why B cannot be zero.

Scale a ratio

A : B → (A × k) : (B × k)

Multiplying both sides by the same factor preserves the ratio.

Variable definitions

Symbol	Meaning	Unit
A	First term. the left-hand side of the ratio	—
B	Second term. the right-hand side; cannot be zero	—
k	Scale factor. the factor both sides are multiplied by	—

Step-by-step calculation

1. Enter both terms
B must be non-zero, since every operation divides by it.
2. Choose the operation
Simplify, convert to decimal or percentage, or scale by a factor.

Limitations

A ratio and a fraction of the whole are different things. A ratio of 1 : 3 means one part in four, not one third — a common source of error in mixing and dilution.
Simplification to lowest terms uses the greatest common divisor, which is exact for whole numbers; decimal inputs are handled numerically and may round.

Calculator inputs

Ratio Input

Your results

Methodology

Formula & methodology

Formula used

Simplify a ratio

Ratio as a decimal or percentage

Scale a ratio

Variable definitions

Step-by-step calculation

Limitations

What is a ratio and how do I simplify it?

How do I convert a ratio to a decimal or percentage?

What does it mean to scale a ratio?

What's the difference between a ratio and a proportion?

How do I check if two ratios are equivalent?

Related calculators

More everyday calculators

Calculator inputs

Ratio Input

Your results

Methodology

How to Use This Calculator

Example: Simplify 10:15

Understanding Your Results

Key Tips

How Ratios Work

What Is a Ratio?

Simplifying and Scaling Ratios

Comparing Ratios Using Decimals and Percentages

Mistake 1: Confusing Ratio Order (a:b vs b:a

Mistake 2: Using Zero or Negative Numbers

Mistake 3: Forgetting to Simplify Ratios

Mistake 4: Miscalculating Scale Factors

Mistake 5: Mixing Different Units Without Conversion

Mistake 6: Not Understanding Decimal & Percentage Conversions

Mistake 7: Ignoring Rounding Errors in Manual Calculations

Mistake 8: Applying Recipe Ratios to Non-Proportional Elements

Ratio Calculator Best Practices Checklist

What is a Ratio Calculator?

Why Ratios Matter

Real-World Applications of Ratio Calculators

Key Benefits of Using Our Ratio Calculator

Example 1: Photography Aspect Ratio Conversion

Example 2: Recipe Ingredient Ratio Scaling

Example 3: Debt-to-Equity Financial Ratio

Example 4: Architectural Blueprint Scaling

Fundamental Ratio Formula

Simplifying Ratios Using GCD

Scaling Ratios by a Factor

Converting Ratios to Decimals & Percentages

Finding Equivalent Ratios

Key Mathematical Principles

Step-by-Step Guide

Real-World Example: Scaling a Recipe

Pro Tip: Common Ratio Patterns

Formula & methodology

Formula used

Simplify a ratio

Ratio as a decimal or percentage

Scale a ratio

Variable definitions

Step-by-step calculation

Limitations

How to Use This Calculator

Example: Simplify 10:15

Understanding Your Results

Key Tips

How Ratios Work

What Is a Ratio?

Simplifying and Scaling Ratios

Comparing Ratios Using Decimals and Percentages

Mistake 1: Confusing Ratio Order (a:b vs b:a

Mistake 2: Using Zero or Negative Numbers

Mistake 3: Forgetting to Simplify Ratios

Mistake 4: Miscalculating Scale Factors

Mistake 5: Mixing Different Units Without Conversion

Mistake 6: Not Understanding Decimal & Percentage Conversions

Mistake 7: Ignoring Rounding Errors in Manual Calculations