math calculator

Decimal to Fraction Calculator

Use our free decimal to fraction calculator to convert any decimal to a fraction. Shows step-by-step work for terminating and repeating decimals.

Formula Verified by Dr. Elena Rostova, PhD

Quick actions: Save inputs, view saved runs, print, share, or export results

Saved Runs

Inputs

Enter Terminating Decimal

Decimal Value

Woodworking & DIY Inches fractions Quick-Select

Select standard fractional inch points to automatically calculate simplified denominators.

Results

Simplified Fraction

GCD Common Divisor125

Equivalent Ratio3 : 8

Proportion Visual

Pie Shading: 3 of 8 equal slices.

Algebraic Conversion Proof

Count the decimal places: There are 3 digits after the decimal point.

Write the decimal as a fraction with a denominator of \(10^{3}\), which equals 1000:

\[x = \frac{375}{1000}\]

Compute the Greatest Common Divisor (GCD) of 375 and 1000 using the Euclidean Algorithm:

\[\text{GCD}(375, 1000) = 125\]

Divide both numerator and denominator by their GCD (125) to reduce the fraction to simplest form:

\[x = \frac{375 \div 125}{1000 \div 125} = \frac{3}{8}\]

Save this math converter

Bookmark this tool for instant fractional measurements on construction sites, kitchen counters, or homework checkups.

Formula

Decimal to Fraction Formulas

Terminating Decimal: x = Numerator / 10^k
Repeating Decimal: (10^(k+p) - 10^k)x = Difference

Terminating decimals are written over positive powers of 10 and simplified via Greatest Common Divisors. Repeating decimals require an algebraic system to cancel recurring fractional parts.

Step by step

How the calculation works

1Terminating decimals represent numbers that end, such as 0.125. We divide by the appropriate base-10 value.
2Repeating decimals repeat a recurring block of digits infinitely, like 0.1666... We isolate the recurrence using algebraic equations.
3Simplify all generated fractions to their lowest terms using Euclidean Greatest Common Divisor factorization.

Related guides

Learn more about this calculation

Guide

Fraction Operations Guide: Add, Subtract, Multiply, Divide

Learn the rules for adding, subtracting, multiplying, and dividing fractions, with simplification steps and live DTC calculator workflows.

Guide

Ratio and Proportion Guide: Simplify, Solve, Split Totals

Learn how to simplify ratios, solve proportions, and split totals with worked examples tied to the live DTC ratio calculator.

Fraction-to-Decimal

Fraction to Decimal

Convert standard numerator/denominator ratios to floating decimals.

Fraction Arithmetic

Fraction Calculator

Add, subtract, multiply, and divide fractions step-by-step.

Mixed Fraction

Mixed Number Fraction

Evaluate operations with whole numbers and fractional parts.

Equivalents

Fraction, Percentage, & Decimal

Convert values between fraction, percent, and decimal forms.

Inputs

Enter Terminating Decimal

Decimal Value

Woodworking & DIY Inches fractions Quick-Select

Select standard fractional inch points to automatically calculate simplified denominators.

Results

Simplified Fraction

GCD Common Divisor125

Equivalent Ratio3 : 8

Proportion Visual

Pie Shading: 3 of 8 equal slices.

Algebraic Conversion Proof

Count the decimal places: There are 3 digits after the decimal point.

Write the decimal as a fraction with a denominator of \(10^{3}\), which equals 1000:

\[x = \frac{375}{1000}\]

Compute the Greatest Common Divisor (GCD) of 375 and 1000 using the Euclidean Algorithm:

\[\text{GCD}(375, 1000) = 125\]

Divide both numerator and denominator by their GCD (125) to reduce the fraction to simplest form:

\[x = \frac{375 \div 125}{1000 \div 125} = \frac{3}{8}\]

How to understand and use this calculator

Quick Answer: How to Change a Decimal to a Fraction

For terminating decimals:

1. Write the decimal as a fraction with denominator 1 (e.g., 0.125 = 0.125 / 1).

2. Multiply numerator and denominator by 10 for each decimal place (e.g., multiply by 1000 for 3 decimal places to get 125/1000).

3. Simplify the fraction to its lowest terms (e.g., 125/1000 = 1/8).

For repeating decimals:

0.333... = 1/3
0.6252525... = 619/990

Quick reference equivalents:

0.5 = 1/2
0.25 = 1/4
0.75 = 3/4
0.125 = 1/8
0.333... = 1/3
0.666... = 2/3

Use the Decimal to Fraction Calculator

To use the calculator:

1. Enter the decimal number you want to convert.

2. Select if the decimal is terminating or repeating (optional).

3. Click "Calculate" or review the live results.

4. Review the fraction, simplified fraction, and step-by-step work.

Example Input (Terminating Decimal):

Decimal: 0.125 | Type: Terminating
Resulting Fraction: 125/1000 | Simplified Fraction: 1/8

Example Input (Repeating Decimal):

Decimal: 0.333... | Type: Repeating
Resulting Fraction: 1/3 with step-by-step algebraic proof.

What is a Decimal to Fraction Conversion?

A decimal to fraction conversion is the process of rewriting a decimal number as a fraction—a ratio of two integers (numerator and denominator).

The basic idea is that every terminating or repeating decimal can be written as a fraction where the denominator is a power of 10 or resolves algebraically. The fraction is then simplified to its lowest terms.

Terminating decimal: A decimal that ends (e.g., 0.125 = 1/8).
Repeating decimal: A decimal that repeats a pattern of digits infinitely (e.g., 0.333... = 1/3).
Numerator: The top number of a fraction (which you can evaluate on our Fraction Calculator).
Denominator: The bottom number of a fraction, representing the total equal parts.

Why Convert Decimals to Fractions?

Exact values: Fractions give exact values, whereas decimals often round. For example, 1/3 is exact, but 0.333... is an approximation (check conversions instantly with our Fraction to Decimal Calculator).
Math operations: Performing arithmetic like multiplying fractions is often cleaner (e.g., 1/3 × 1/4 = 1/12).
Real-world measurements: Construction, cooking, and drafting use fractional inches or cups (e.g., 1/4 inch, 1/2 cup).
Comparisons: Fractions can be easier to compare at a glance once they share a common denominator.

Real-world example: If you have 0.166... of a pizza and there are 6 people, it's much easier to visualize it as exactly 1/6 of the pizza per person.

How to Convert a Terminating Decimal to a Fraction — Step by Step

Step 1: Write the decimal as a fraction with denominator 1. For example: 0.125 = 0.125 / 1.
Step 2: Count the decimal places. 0.125 has 3 digits after the decimal point.
Step 3: Multiply numerator and denominator by 10 for each place. For 3 decimal places, multiply by 1000 (10³): 0.125/1 × 1000/1000 = 125/1000.
Step 4: Simplify the fraction. Find the greatest common factor (GCF) of 125 and 1000, which is 125. Divide both numbers: 125 ÷ 125 = 1 and 1000 ÷ 125 = 8 to get 1/8.

Worked examples:

0.75: 2 decimal places → 75/100. GCF = 25 → 3/4.
1.25: 2 decimal places → 125/100. GCF = 25 → 5/4 (or 1 1/4 as a mixed number).
0.625: 3 decimal places → 625/1000. GCF = 125 → 5/8.

How to Convert a Repeating Decimal to a Fraction — Step by Step

Converting repeating decimals uses algebra to eliminate the infinite recurring digits:

Step 1: Let x equal the repeating decimal: x = 0.333...
Step 2: Multiply x by 10 for each repeating digit. One repeating digit means multiplying by 10: 10x = 3.333...
Step 3: Subtract the original equation: 10x − x = 3.333... − 0.333... which gives 9x = 3.
Step 4: Solve for x: x = 3/9, which simplifies to 1/3.

Worked examples:

0.666... (repeating 6): 10x = 6.666... → 9x = 6 → x = 6/9 = 2/3.
0.125125... (repeating 125): 3 repeating digits → multiply by 1000: 1000x = 125.125... → 999x = 125 → x = 125/999.
0.6252525... (repeating 25): 2 repeating digits → multiply by 100: 100x = 62.525... Subtracting x gives 99x = 61.9. Multiply by 10: 990x = 619 → x = 619/990.

How to Simplify a Fraction

Method 1: Find the Greatest Common Factor (GCF). List factors of the numerator and denominator, identify the largest shared factor, and divide both parts by it. For 125/1000, GCF = 125, which reduces it to 1/8.
Method 2: Repeated Division. Divide the numerator and denominator by any obvious common factors (like 2 or 5) and repeat until no common factors remain. E.g., 125/1000 ÷ 5 = 25/200; ÷ 5 = 5/40; ÷ 5 = 1/8.

How to Convert an Improper Fraction to a Mixed Number

An improper fraction has a numerator larger than or equal to the denominator. To easily convert between these forms, try our Mixed Number Fraction Calculator.

1. Divide the numerator by the denominator (5 ÷ 4 = 1 with a remainder of 1).

2. The quotient (1) is the whole number.

3. The remainder (1) becomes the new numerator, placed over the same denominator (4) to get 1 1/4.

5/4 → 5 ÷ 4 = 1 R1 → 1 1/4
7/3 → 7 ÷ 3 = 2 R1 → 2 1/3
11/2 → 11 ÷ 2 = 5 R1 → 5 1/2
9/4 → 9 ÷ 4 = 2 R1 → 2 1/4

How to Use This Calculator for Inches and Fractions

In woodworking, construction, and DIY, decimal measurements must be converted to standard fractional inches:

0.0625 = 1/16 in
0.125 = 1/8 in
0.25 = 1/4 in
0.375 = 3/8 in
0.5 = 1/2 in
0.625 = 5/8 in
0.75 = 3/4 in
0.875 = 7/8 in

Simply enter the decimal part of your measurement (e.g. 0.75 in 2.75 inches) into the calculator to get the fraction (3/4), giving you 2 3/4 inches.

How to Use This Calculator for Fractions in Operations

If you need to perform calculations like 4 3/5 × 2/3:

1. Convert mixed numbers to improper fractions: 4 3/5 = (4 × 5 + 3)/5 = 23/5.

2. Multiply the fractions: 23/5 × 2/3 = (23 × 2) / (5 × 3) = 46/15.

3. Convert back to a mixed number: 46 ÷ 15 = 3 with remainder 1 → 3 1/15.

Practice Problems

Problem 1: Convert 0.625 to a fraction.

Solution: 0.625 × 1000 = 625/1000. GCF = 125. Divide to get 5/8.

Problem 2: Convert 0.75 to a fraction.

Solution: 0.75 × 100 = 75/100. GCF = 25. Divide to get 3/4.

Problem 3: Convert 0.333... (repeating 3) to a fraction.

Solution: x = 0.333...; 10x = 3.333...; subtracting gives 9x = 3; x = 3/9 = 1/3.

Problem 4: Convert 1.25 to a fraction and mixed number.

Solution: 1.25 × 100 = 125/100. GCF = 25. Divide to get 5/4. Mixed number: 1 1/4.

Problem 5: Convert 0.727272... (repeating 72) to a fraction.

Solution: x = 0.727272...; 100x = 72.727272...; subtracting gives 99x = 72; x = 72/99. GCF = 9. Divide to get 8/11.

Common Decimal to Fraction Mistakes

Counting decimal places incorrectly: Miscounting 0.125 as 2 decimal places instead of 3, leading to 125/100 (incorrect) instead of 125/1000.
Not simplifying the fraction: Leaving the result as 125/1000 instead of reducing it to its simplest form, 1/8.
Forgetting to multiply both sides: Multiplying only the numerator (e.g., writing 0.125 = 125/1). You must multiply BOTH numerator and denominator by the same power of 10.
Confusing terminating and repeating decimals: Using the terminating method for repeating numbers, which gives incorrect ratios (e.g., treating 0.333... as 333/1000 instead of using the algebraic proof to get 1/3).
Not simplifying repeating decimal fractions: Leaving the recurring solution as 6/9 instead of simplifying to 2/3.
Misplacing the decimal point: Converting 0.125 to 1250/1000 by accident.
Forgetting to convert with the right power of 10: Writing 0.75 as 75/10 (wrong) instead of 75/100.
Not checking the answer: Assuming the result is correct without dividing it back out to verify.

What This Calculator Can and Cannot Do

This calculator CAN help with:

Converting terminating decimals to fractions.
Converting repeating decimals to fractions.
Simplifying fractions to their lowest terms.
Converting improper fractions to mixed numbers.
Quick woodworking inch-to-fraction conversions.
Perform complex matrix or equation operations.
Convert fractions to decimals (use our Fraction to Decimal Calculator instead).
Perform direct arithmetic operations like addition or multiplication of fractions.
Handle percentages directly (use our Fraction, Percentage, & Decimal Calculator or Percentage Calculator instead).
Convert decimals with exponents.

Final Summary

A decimal to fraction calculator is essential for anyone working with numbers—whether you're a student, teacher, professional, or DIY enthusiast. Converting decimals to fractions gives you exact values that are easier to work with in math, measurements, and real-world applications.

Remember the key steps:

Terminating decimal: Count decimal places, multiply by 10^n, simplify.
Repeating decimal: Use the algebra method (x = decimal, multiply, subtract, solve).
Simplify: Find the GCF and divide both numerator and denominator.

Quick reference: 0.125 = 1/8, 0.25 = 1/4, 0.333... = 1/3, 0.5 = 1/2, 0.625 = 5/8, 0.75 = 3/4.

Start converting now! Just enter your decimal above and get instant results—completely free.

Related concepts

Fraction Calculator

Perform addition, subtraction, multiplication, and division of fractions.

Fraction to Decimal Calculator

Convert fraction ratios back into decimal numbers.

Percentage Calculator

Convert fractions and decimals to percentage values.

Long Division Calculator

Compute divisions step-by-step with remainders.

Frequently Asked Questions

What is a decimal to fraction calculator?+

A decimal to fraction calculator converts any decimal number into its equivalent fraction form. It handles both terminating and repeating decimals.

How do you change a decimal to a fraction?+

To change a decimal to a fraction, write the decimal as a fraction with denominator 1, multiply by 10 for each decimal place, then simplify the fraction.

What is 0.125 as a fraction?+

0.125 as a fraction is 1/8. To convert: 0.125 = 125/1000, then simplify by dividing by 125 → 1/8.

What is 0.333... as a fraction?+

0.333... (repeating 3) as a fraction is 1/3. This is one of the most common repeating decimals.

What is 0.625 as a fraction?+

0.625 as a fraction is 5/8. To convert: 0.625 × 1000 = 625/1000, simplify by dividing by 125 → 5/8.

What is 0.75 as a fraction?+

0.75 as a fraction is 3/4. To convert: 0.75 × 100 = 75/100, simplify by dividing by 25 → 3/4.

What is 1.25 as a fraction?+

1.25 as a fraction is 5/4 (or 1 1/4 as a mixed number).

How do you convert a repeating decimal to a fraction?+

Use the algebra method: set x = the repeating decimal, multiply by 10 for each repeating digit, subtract the original, and solve for x.

What is 0.6252525... as a fraction?+

0.6252525... (repeating 25) as a fraction is 619/990.

What is 0.9999... as a fraction?+

0.9999... (repeating 9) as a fraction is 1. This is a mathematical fact: 0.9999... = 1.

How do you use a calculator with fractions?+

A fraction calculator allows you to perform operations like addition, subtraction, multiplication, and division with fractions. Enter the numerator and denominator for each fraction, choose the operation, and get the result.

How do you simplify a fraction?+

To simplify a fraction, find the greatest common factor (GCF) of the numerator and denominator, then divide both by the GCF.

What is the difference between terminating and repeating decimals?+

A terminating decimal ends (e.g., 0.125). A repeating decimal repeats forever (e.g., 0.333...). Both can be converted to fractions.

What is 4 3/5 x 2/3?+

4 3/5 × 2/3 = 23/5 × 2/3 = 46/15 = 3 1/15.

What is a simplified fraction calculator?+

A simplified fraction calculator reduces any fraction to its lowest terms by finding and dividing by the greatest common factor.

Is this decimal to fraction calculator free?+

Yes — completely free with no registration required.

How the calculation works

1Terminating decimals represent numbers that end, such as 0.125. We divide by the appropriate base-10 value.

2Repeating decimals repeat a recurring block of digits infinitely, like 0.1666... We isolate the recurrence using algebraic equations.

3Simplify all generated fractions to their lowest terms using Euclidean Greatest Common Divisor factorization.

How to understand and use this calculator

Quick Answer: How to Change a Decimal to a Fraction

For terminating decimals:

1. Write the decimal as a fraction with denominator 1 (e.g., 0.125 = 0.125 / 1).

2. Multiply numerator and denominator by 10 for each decimal place (e.g., multiply by 1000 for 3 decimal places to get 125/1000).

3. Simplify the fraction to its lowest terms (e.g., 125/1000 = 1/8).

For repeating decimals:

0.333... = 1/3
0.6252525... = 619/990

Quick reference equivalents:

0.5 = 1/2
0.25 = 1/4
0.75 = 3/4
0.125 = 1/8
0.333... = 1/3
0.666... = 2/3

Use the Decimal to Fraction Calculator

To use the calculator:

1. Enter the decimal number you want to convert.

2. Select if the decimal is terminating or repeating (optional).

3. Click "Calculate" or review the live results.

4. Review the fraction, simplified fraction, and step-by-step work.

Example Input (Terminating Decimal):

Decimal: 0.125 | Type: Terminating
Resulting Fraction: 125/1000 | Simplified Fraction: 1/8

Example Input (Repeating Decimal):

Decimal: 0.333... | Type: Repeating
Resulting Fraction: 1/3 with step-by-step algebraic proof.

What is a Decimal to Fraction Conversion?

A decimal to fraction conversion is the process of rewriting a decimal number as a fraction—a ratio of two integers (numerator and denominator).

Terminating decimal: A decimal that ends (e.g., 0.125 = 1/8).
Repeating decimal: A decimal that repeats a pattern of digits infinitely (e.g., 0.333... = 1/3).
Numerator: The top number of a fraction (which you can evaluate on our Fraction Calculator).
Denominator: The bottom number of a fraction, representing the total equal parts.

Why Convert Decimals to Fractions?

Exact values: Fractions give exact values, whereas decimals often round. For example, 1/3 is exact, but 0.333... is an approximation (check conversions instantly with our Fraction to Decimal Calculator).
Math operations: Performing arithmetic like multiplying fractions is often cleaner (e.g., 1/3 × 1/4 = 1/12).
Real-world measurements: Construction, cooking, and drafting use fractional inches or cups (e.g., 1/4 inch, 1/2 cup).
Comparisons: Fractions can be easier to compare at a glance once they share a common denominator.

Real-world example: If you have 0.166... of a pizza and there are 6 people, it's much easier to visualize it as exactly 1/6 of the pizza per person.

How to Convert a Terminating Decimal to a Fraction — Step by Step

Step 1: Write the decimal as a fraction with denominator 1. For example: 0.125 = 0.125 / 1.
Step 2: Count the decimal places. 0.125 has 3 digits after the decimal point.
Step 3: Multiply numerator and denominator by 10 for each place. For 3 decimal places, multiply by 1000 (10³): 0.125/1 × 1000/1000 = 125/1000.
Step 4: Simplify the fraction. Find the greatest common factor (GCF) of 125 and 1000, which is 125. Divide both numbers: 125 ÷ 125 = 1 and 1000 ÷ 125 = 8 to get 1/8.

Worked examples:

0.75: 2 decimal places → 75/100. GCF = 25 → 3/4.
1.25: 2 decimal places → 125/100. GCF = 25 → 5/4 (or 1 1/4 as a mixed number).
0.625: 3 decimal places → 625/1000. GCF = 125 → 5/8.

How to Convert a Repeating Decimal to a Fraction — Step by Step

Converting repeating decimals uses algebra to eliminate the infinite recurring digits:

Step 1: Let x equal the repeating decimal: x = 0.333...
Step 2: Multiply x by 10 for each repeating digit. One repeating digit means multiplying by 10: 10x = 3.333...
Step 3: Subtract the original equation: 10x − x = 3.333... − 0.333... which gives 9x = 3.
Step 4: Solve for x: x = 3/9, which simplifies to 1/3.

Worked examples:

0.666... (repeating 6): 10x = 6.666... → 9x = 6 → x = 6/9 = 2/3.
0.125125... (repeating 125): 3 repeating digits → multiply by 1000: 1000x = 125.125... → 999x = 125 → x = 125/999.
0.6252525... (repeating 25): 2 repeating digits → multiply by 100: 100x = 62.525... Subtracting x gives 99x = 61.9. Multiply by 10: 990x = 619 → x = 619/990.

How to Simplify a Fraction

Method 1: Find the Greatest Common Factor (GCF). List factors of the numerator and denominator, identify the largest shared factor, and divide both parts by it. For 125/1000, GCF = 125, which reduces it to 1/8.
Method 2: Repeated Division. Divide the numerator and denominator by any obvious common factors (like 2 or 5) and repeat until no common factors remain. E.g., 125/1000 ÷ 5 = 25/200; ÷ 5 = 5/40; ÷ 5 = 1/8.

How to Convert an Improper Fraction to a Mixed Number

An improper fraction has a numerator larger than or equal to the denominator. To easily convert between these forms, try our Mixed Number Fraction Calculator.

1. Divide the numerator by the denominator (5 ÷ 4 = 1 with a remainder of 1).

2. The quotient (1) is the whole number.

3. The remainder (1) becomes the new numerator, placed over the same denominator (4) to get 1 1/4.

5/4 → 5 ÷ 4 = 1 R1 → 1 1/4
7/3 → 7 ÷ 3 = 2 R1 → 2 1/3
11/2 → 11 ÷ 2 = 5 R1 → 5 1/2
9/4 → 9 ÷ 4 = 2 R1 → 2 1/4

How to Use This Calculator for Inches and Fractions

In woodworking, construction, and DIY, decimal measurements must be converted to standard fractional inches:

0.0625 = 1/16 in
0.125 = 1/8 in
0.25 = 1/4 in
0.375 = 3/8 in
0.5 = 1/2 in
0.625 = 5/8 in
0.75 = 3/4 in
0.875 = 7/8 in

Simply enter the decimal part of your measurement (e.g. 0.75 in 2.75 inches) into the calculator to get the fraction (3/4), giving you 2 3/4 inches.

How to Use This Calculator for Fractions in Operations

If you need to perform calculations like 4 3/5 × 2/3:

1. Convert mixed numbers to improper fractions: 4 3/5 = (4 × 5 + 3)/5 = 23/5.

2. Multiply the fractions: 23/5 × 2/3 = (23 × 2) / (5 × 3) = 46/15.

3. Convert back to a mixed number: 46 ÷ 15 = 3 with remainder 1 → 3 1/15.

Practice Problems

Problem 1: Convert 0.625 to a fraction.

Solution: 0.625 × 1000 = 625/1000. GCF = 125. Divide to get 5/8.

Problem 2: Convert 0.75 to a fraction.

Solution: 0.75 × 100 = 75/100. GCF = 25. Divide to get 3/4.

Problem 3: Convert 0.333... (repeating 3) to a fraction.

Solution: x = 0.333...; 10x = 3.333...; subtracting gives 9x = 3; x = 3/9 = 1/3.

Problem 4: Convert 1.25 to a fraction and mixed number.

Solution: 1.25 × 100 = 125/100. GCF = 25. Divide to get 5/4. Mixed number: 1 1/4.

Problem 5: Convert 0.727272... (repeating 72) to a fraction.

Solution: x = 0.727272...; 100x = 72.727272...; subtracting gives 99x = 72; x = 72/99. GCF = 9. Divide to get 8/11.

Common Decimal to Fraction Mistakes

Counting decimal places incorrectly: Miscounting 0.125 as 2 decimal places instead of 3, leading to 125/100 (incorrect) instead of 125/1000.
Not simplifying the fraction: Leaving the result as 125/1000 instead of reducing it to its simplest form, 1/8.
Forgetting to multiply both sides: Multiplying only the numerator (e.g., writing 0.125 = 125/1). You must multiply BOTH numerator and denominator by the same power of 10.
Confusing terminating and repeating decimals: Using the terminating method for repeating numbers, which gives incorrect ratios (e.g., treating 0.333... as 333/1000 instead of using the algebraic proof to get 1/3).
Not simplifying repeating decimal fractions: Leaving the recurring solution as 6/9 instead of simplifying to 2/3.
Misplacing the decimal point: Converting 0.125 to 1250/1000 by accident.
Forgetting to convert with the right power of 10: Writing 0.75 as 75/10 (wrong) instead of 75/100.
Not checking the answer: Assuming the result is correct without dividing it back out to verify.

What This Calculator Can and Cannot Do

This calculator CAN help with:

Converting terminating decimals to fractions.
Converting repeating decimals to fractions.
Simplifying fractions to their lowest terms.
Converting improper fractions to mixed numbers.
Quick woodworking inch-to-fraction conversions.
Perform complex matrix or equation operations.
Convert fractions to decimals (use our Fraction to Decimal Calculator instead).
Perform direct arithmetic operations like addition or multiplication of fractions.
Handle percentages directly (use our Fraction, Percentage, & Decimal Calculator or Percentage Calculator instead).
Convert decimals with exponents.

Final Summary

Remember the key steps:

Terminating decimal: Count decimal places, multiply by 10^n, simplify.
Repeating decimal: Use the algebra method (x = decimal, multiply, subtract, solve).
Simplify: Find the GCF and divide both numerator and denominator.

Quick reference: 0.125 = 1/8, 0.25 = 1/4, 0.333... = 1/3, 0.5 = 1/2, 0.625 = 5/8, 0.75 = 3/4.

Start converting now! Just enter your decimal above and get instant results—completely free.

Related concepts

Fraction Calculator

Perform addition, subtraction, multiplication, and division of fractions.

Fraction to Decimal Calculator

Convert fraction ratios back into decimal numbers.

Percentage Calculator

Convert fractions and decimals to percentage values.

Long Division Calculator

Compute divisions step-by-step with remainders.

Frequently Asked Questions

What is a decimal to fraction calculator?+

A decimal to fraction calculator converts any decimal number into its equivalent fraction form. It handles both terminating and repeating decimals.

How do you change a decimal to a fraction?+

To change a decimal to a fraction, write the decimal as a fraction with denominator 1, multiply by 10 for each decimal place, then simplify the fraction.

What is 0.125 as a fraction?+

0.125 as a fraction is 1/8. To convert: 0.125 = 125/1000, then simplify by dividing by 125 → 1/8.

What is 0.333... as a fraction?+

0.333... (repeating 3) as a fraction is 1/3. This is one of the most common repeating decimals.

What is 0.625 as a fraction?+

0.625 as a fraction is 5/8. To convert: 0.625 × 1000 = 625/1000, simplify by dividing by 125 → 5/8.

What is 0.75 as a fraction?+

0.75 as a fraction is 3/4. To convert: 0.75 × 100 = 75/100, simplify by dividing by 25 → 3/4.

What is 1.25 as a fraction?+

1.25 as a fraction is 5/4 (or 1 1/4 as a mixed number).

How do you convert a repeating decimal to a fraction?+

Use the algebra method: set x = the repeating decimal, multiply by 10 for each repeating digit, subtract the original, and solve for x.

What is 0.6252525... as a fraction?+

0.6252525... (repeating 25) as a fraction is 619/990.

What is 0.9999... as a fraction?+

0.9999... (repeating 9) as a fraction is 1. This is a mathematical fact: 0.9999... = 1.

How do you use a calculator with fractions?+

How do you simplify a fraction?+

To simplify a fraction, find the greatest common factor (GCF) of the numerator and denominator, then divide both by the GCF.

What is the difference between terminating and repeating decimals?+

A terminating decimal ends (e.g., 0.125). A repeating decimal repeats forever (e.g., 0.333...). Both can be converted to fractions.

What is 4 3/5 x 2/3?+

4 3/5 × 2/3 = 23/5 × 2/3 = 46/15 = 3 1/15.

What is a simplified fraction calculator?+

A simplified fraction calculator reduces any fraction to its lowest terms by finding and dividing by the greatest common factor.

Is this decimal to fraction calculator free?+

Yes — completely free with no registration required.

Decimal to Fraction Calculator

Inputs

Enter Terminating Decimal

Woodworking & DIY Inches fractions Quick-Select

Results

Proportion Visual

Algebraic Conversion Proof

Save this math converter

Decimal to Fraction Formulas

How the calculation works

Learn more about this calculation

Fraction Operations Guide: Add, Subtract, Multiply, Divide

Ratio and Proportion Guide: Simplify, Solve, Split Totals

Fraction to Decimal

Fraction Calculator

Mixed Number Fraction

Fraction, Percentage, & Decimal

Decimal to Fraction Calculator

Inputs

Enter Terminating Decimal

Woodworking & DIY Inches fractions Quick-Select

Results

Proportion Visual

Algebraic Conversion Proof

Save this math converter

Key output metrics

How to understand and use this calculator

Quick Answer: How to Change a Decimal to a Fraction

Use the Decimal to Fraction Calculator

What is a Decimal to Fraction Conversion?

Why Convert Decimals to Fractions?

How to Convert a Terminating Decimal to a Fraction — Step by Step

How to Convert a Repeating Decimal to a Fraction — Step by Step

How to Simplify a Fraction

How to Convert an Improper Fraction to a Mixed Number

How to Use This Calculator for Inches and Fractions

How to Use This Calculator for Fractions in Operations

Practice Problems

Common Decimal to Fraction Mistakes

What This Calculator Can and Cannot Do

Final Summary

Related concepts

Frequently Asked Questions

Decimal to Fraction Formulas

How the calculation works

Learn more about this calculation

Fraction Operations Guide: Add, Subtract, Multiply, Divide

Ratio and Proportion Guide: Simplify, Solve, Split Totals

Fraction to Decimal

Fraction Calculator

Mixed Number Fraction

Fraction, Percentage, & Decimal

Key output metrics

How to understand and use this calculator

Quick Answer: How to Change a Decimal to a Fraction

Use the Decimal to Fraction Calculator

What is a Decimal to Fraction Conversion?

Why Convert Decimals to Fractions?

How to Convert a Terminating Decimal to a Fraction — Step by Step

How to Convert a Repeating Decimal to a Fraction — Step by Step

How to Simplify a Fraction

How to Convert an Improper Fraction to a Mixed Number

How to Use This Calculator for Inches and Fractions

How to Use This Calculator for Fractions in Operations

Practice Problems

Common Decimal to Fraction Mistakes

What This Calculator Can and Cannot Do

Final Summary

Related concepts

Frequently Asked Questions