# How to Convert Decimals to Fractions Manually: Step-by-Step Guide

Write the decimal over 1, multiply top and bottom by 10 for each decimal place, then simplify by the greatest common factor. Step-by-step methods for terminating and repeating decimals, worked examples, practice problems and a conversion chart.

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- **Canonical URL:** https://dothecalculation.com/blog/math/how-to-convert-decimals-to-fractions
- **Category:** Math
- **Author:** Do The Calculation Team
- **Published:** 2026-09-22
- **Reading time:** 10 min read
- **Publisher:** Do The Calculation (https://dothecalculation.com)
- **Methodology:** https://dothecalculation.com/methodology

---

## How to Convert Decimals to Fractions Manually

Converting decimals to fractions is one of the most useful math skills you can learn. Whether you are a student working on homework, a teacher preparing a lesson, or someone who wants to understand the math behind the calculator, this guide walks you through every step.

Many people rely on a decimal to fraction calculator for quick answers. Knowing how to do it by hand gives you a deeper grasp of the math and lets you check your work with confidence.

In this guide, you will learn:

- What decimals and fractions are, in simple terms
- How to convert terminating decimals to fractions, step by step
- How to convert repeating decimals to fractions, step by step
- How to simplify fractions, the key final step
- Worked examples at different difficulty levels
- Practice problems with answers
- Common mistakes and how to avoid them

Tool: [Try the Decimal to Fraction Calculator](https://dothecalculation.com/calculators/decimal-to-fraction-calculator) — Convert terminating or repeating decimals to simplified fractions and see the GCF steps, so you can check every answer in this guide.

## Quick Answer: How Do You Convert a Decimal to a Fraction?

To convert a decimal to a fraction manually:

- Write the decimal as a fraction with denominator 1.
- Multiply the numerator and denominator by 10 for each decimal place.
- Simplify the fraction by dividing both parts by their greatest common factor (GCF).

**Simple example**

```
0.125 → 125/1000 → divide both by 125 → 1/8
```

**Quick reference**
| Decimal | Fraction | Simplified |
| --- | --- | --- |
| 0.5 | 5/10 | 1/2 |
| 0.25 | 25/100 | 1/4 |
| 0.75 | 75/100 | 3/4 |
| 0.125 | 125/1000 | 1/8 |
| 0.333... | 3/9 | 1/3 |
| 0.666... | 6/9 | 2/3 |

> **Key insight** — Every terminating or repeating decimal can be written as a fraction. The process is simple once you know the steps.

## What Is a Decimal?

A decimal is a number written in the base-10 system, with a decimal point separating the whole-number part from the parts of a whole. The digits after the point are tenths, hundredths, thousandths and so on.

- 0.5 means 5 tenths
- 0.25 means 25 hundredths
- 0.125 means 125 thousandths

**Place values in decimals**
| Place | Value | Example |
| --- | --- | --- |
| Tenths | 1/10 | 0.5 = 5 tenths |
| Hundredths | 1/100 | 0.25 = 25 hundredths |
| Thousandths | 1/1000 | 0.125 = 125 thousandths |
| Ten-thousandths | 1/10000 | 0.0625 = 625 ten-thousandths |

**Types of decimals**
| Type | Description | Example |
| --- | --- | --- |
| Terminating | Ends after a certain number of digits | 0.125, 0.75, 0.5 |
| Repeating | Repeats a pattern of digits forever | 0.333..., 0.666..., 0.125125... |

Place value is the whole trick behind the terminating method: the last decimal place tells you the denominator. If division and remainders are where your decimals come from, [long division answers: remainder, decimal or fraction](/blog/math/long-division-remainder-decimal-fraction-guide) shows how the same quotient can be written all three ways.

## What Is a Fraction?

A fraction represents a part of a whole. It has two parts:

- Numerator: the top number, how many parts you have.
- Denominator: the bottom number, how many equal parts the whole is divided into.

- 1/2 means 1 part out of 2 equal parts
- 3/4 means 3 parts out of 4 equal parts

### Why convert decimals to fractions?

- Fractions give exact values, while written-out decimals are often rounded.
- Fractions are easier to work with in some calculations, such as multiplying by 1/3.
- Fractions are used in measurements, from cooking to construction.
- Fractions are easier to compare in some situations.

For example, 0.333 (stopped after three digits) is only an approximation, and 0.333... with the 3s repeating forever is exactly 1/3. Writing 1/3 is shorter and carries the exact value without any dots.

## How to Convert a Terminating Decimal to a Fraction

This is the most common type of conversion. Here is how to do it by hand.

### The 4-step method

- Step 1: Write the decimal as a fraction with denominator 1. Example: 0.125 = 0.125/1.
- Step 2: Count the number of decimal places. 0.125 has 3 decimal places.
- Step 3: Multiply the numerator and denominator by 10 for each decimal place. 3 places means multiply by 1000: 0.125/1 × 1000/1000 = 125/1000.
- Step 4: Simplify the fraction. The GCF of 125 and 1000 is 125, and 125 ÷ 125 = 1, 1000 ÷ 125 = 8, so the answer is 1/8.

> **Answer** — 0.125 = 1/8

### Worked example 1: convert 0.75 to a fraction

**0.75 as a fraction**

```
Step 1: 0.75/1
Step 2: 2 decimal places
Step 3: 0.75/1 × 100/100 = 75/100
Step 4: GCF of 75 and 100 = 25 → 75 ÷ 25 = 3, 100 ÷ 25 = 4
```
- 0.75 = 3/4

### Worked example 2: convert 0.625 to a fraction

**0.625 as a fraction**

```
Step 1: 0.625/1
Step 2: 3 decimal places
Step 3: 0.625/1 × 1000/1000 = 625/1000
Step 4: GCF of 625 and 1000 = 125 → 625 ÷ 125 = 5, 1000 ÷ 125 = 8
```
- 0.625 = 5/8

### Worked example 3: convert 1.25 to a fraction

**1.25 as a fraction**

```
Step 1: 1.25/1
Step 2: 2 decimal places
Step 3: 1.25/1 × 100/100 = 125/100
Step 4: GCF of 125 and 100 = 25 → 125 ÷ 25 = 5, 100 ÷ 25 = 4 → 5/4
Step 5 (optional): 5/4 = 1 1/4 as a mixed number
```
- 1.25 = 5/4 or 1 1/4

When the decimal is bigger than 1, you get an improper fraction. To switch between 5/4 and 1 1/4, or to add and subtract answers like these, use the [mixed number calculator](/calculators/mixed-number-calculator).

### Worked example 4: convert 0.0625 to a fraction

**0.0625 as a fraction**

```
Step 1: 0.0625/1
Step 2: 4 decimal places
Step 3: 0.0625/1 × 10000/10000 = 625/10000
Step 4: GCF of 625 and 10000 = 625 → 625 ÷ 625 = 1, 10000 ÷ 625 = 16
```
- 0.0625 = 1/16

## How to Convert a Repeating Decimal to a Fraction

Repeating decimals need a different method, based on a little algebra. Here is how it works.

### The method

- Step 1: Let x equal the repeating decimal. Example: x = 0.333...
- Step 2: Multiply by 10 for each repeating digit. One repeating digit (3) means multiply by 10: 10x = 3.333...
- Step 3: Subtract the original equation from the new one: 10x − x = 3.333... − 0.333..., so 9x = 3. The repeating tails cancel out.
- Step 4: Solve for x: x = 3/9.
- Step 5: Simplify. The GCF of 3 and 9 is 3, so 3 ÷ 3 = 1 and 9 ÷ 3 = 3, giving 1/3.

> **Answer** — 0.333... = 1/3

### Worked example 5: convert 0.666... to a fraction

**0.666... as a fraction**

```
Step 1: x = 0.666...
Step 2: 10x = 6.666...
Step 3: 10x − x = 6.666... − 0.666... → 9x = 6
Step 4: x = 6/9
Step 5: GCF of 6 and 9 = 3 → 6 ÷ 3 = 2, 9 ÷ 3 = 3
```
- 0.666... = 2/3

### Worked example 6: convert 0.125125... to a fraction

**0.125125... as a fraction**

```
Step 1: x = 0.125125...
Step 2: 3 repeating digits → 1000x = 125.125125...
Step 3: 1000x − x = 125.125125... − 0.125125... → 999x = 125
Step 4: x = 125/999
Step 5: GCF of 125 and 999 = 1 → already in simplest form
```
- 0.125125... = 125/999

### Worked example 7: convert 0.6252525... to a fraction

Here only the 25 repeats, and the 6 before it does not. The same method still works; you just clear the leftover decimal at the end.

**0.6252525... as a fraction**

```
Step 1: x = 0.6252525...
Step 2: 2 repeating digits (25) → 100x = 62.5252525...
Step 3: 100x − x = 62.5252525... − 0.6252525... → 99x = 61.9
Step 4: Multiply both sides by 10 to remove the decimal → 990x = 619
Step 5: x = 619/990
Step 6: GCF of 619 and 990 = 1 → already in simplest form
```
- 0.6252525... = 619/990

> **A shortcut you can check against** — When the repeat starts right after the decimal point, the fraction is the repeating digits over the same number of 9s: 0.333... = 3/9, 0.125125... = 125/999, 0.0909... = 09/99 = 9/99. Then simplify as usual.

## How to Simplify Fractions: The Key Final Step

Simplifying is the final and most important step. A fraction like 125/1000 is correct but not finished until it is written as 1/8. There are two easy ways to do it.

### Method 1: find the greatest common factor (GCF)

- Step 1: List the factors of the numerator.
- Step 2: List the factors of the denominator.
- Step 3: Identify the greatest common factor.
- Step 4: Divide both by the GCF.

**Simplify 125/1000 with the GCF**

```
Factors of 125: 1, 5, 25, 125
Factors of 1000: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000
GCF = 125 → 125 ÷ 125 = 1, 1000 ÷ 125 = 8
```
- 125/1000 = 1/8

### Method 2: divide by common factors repeatedly

- Step 1: Divide the numerator and denominator by any common factor.
- Step 2: Repeat until no common factors remain.

**Simplify 125/1000 by repeated division**

```
125/1000 → ÷ 5 → 25/200 → ÷ 5 → 5/40 → ÷ 5 → 1/8
```
- Same answer, reached in three small steps.

For large numbers, listing factors gets slow. Breaking both numbers into primes with the [prime factorization calculator](/calculators/prime-factorization-calculator) shows the common factors at a glance, and [how to simplify fractions step by step](/blog/math/how-to-simplify-fractions-step-by-step-guide) covers the GCF, prime factorization and repeated-division methods in full, with practice questions.

**Quick reference: common fraction simplifications**
| Original | Simplified | GCF |
| --- | --- | --- |
| 5/10 | 1/2 | 5 |
| 25/100 | 1/4 | 25 |
| 75/100 | 3/4 | 25 |
| 125/1000 | 1/8 | 125 |
| 625/1000 | 5/8 | 125 |
| 375/1000 | 3/8 | 125 |
| 875/1000 | 7/8 | 125 |

## Common Decimal to Fraction Conversions

Here is a quick reference for the conversions that come up most often.

**Common terminating decimals**
| Decimal | Fraction | Simplified |
| --- | --- | --- |
| 0.1 | 1/10 | 1/10 |
| 0.2 | 2/10 | 1/5 |
| 0.25 | 25/100 | 1/4 |
| 0.5 | 5/10 | 1/2 |
| 0.75 | 75/100 | 3/4 |
| 0.125 | 125/1000 | 1/8 |
| 0.375 | 375/1000 | 3/8 |
| 0.625 | 625/1000 | 5/8 |
| 0.875 | 875/1000 | 7/8 |
| 0.0625 | 625/10000 | 1/16 |

**Common repeating decimals**
| Decimal | Fraction | Simplified |
| --- | --- | --- |
| 0.333... | 3/9 | 1/3 |
| 0.666... | 6/9 | 2/3 |
| 0.1666... | 15/90 | 1/6 |
| 0.8333... | 75/90 | 5/6 |
| 0.111... | 1/9 | 1/9 |
| 0.222... | 2/9 | 2/9 |
| 0.444... | 4/9 | 4/9 |
| 0.555... | 5/9 | 5/9 |
| 0.777... | 7/9 | 7/9 |
| 0.888... | 8/9 | 8/9 |
| 0.0909... | 9/99 | 1/11 |
| 0.1818... | 18/99 | 2/11 |

To go the other way, from a fraction back to a decimal, divide the numerator by the denominator or use the [fraction to decimal calculator](/calculators/fraction-to-decimal-calculator). If you also need the percentage, the [fraction, percentage and decimal calculator](/calculators/fraction-percentage-decimal-calculator) shows all three forms together.

## Practice Problems (With Answers)

### Problem 1: convert 0.4 to a fraction

**Solution**

```
0.4/1 × 10/10 = 4/10
GCF = 2
```
- 0.4 = 2/5

### Problem 2: convert 0.375 to a fraction

**Solution**

```
0.375/1 × 1000/1000 = 375/1000
GCF = 125
```
- 0.375 = 3/8

### Problem 3: convert 0.666... to a fraction

**Solution**

```
x = 0.666...
10x = 6.666...
9x = 6
x = 6/9 = 2/3
```
- 0.666... = 2/3

### Problem 4: convert 0.5625 to a fraction

**Solution**

```
0.5625/1 × 10000/10000 = 5625/10000
GCF = 625
```
- 0.5625 = 9/16

### Problem 5: convert 2.5 to a fraction and a mixed number

**Solution**

```
2.5/1 × 10/10 = 25/10
GCF = 5 → 25/10 = 5/2
```
- 2.5 = 5/2 = 2 1/2

### Problem 6: convert 0.0909... to a fraction

**Solution**

```
x = 0.0909...
100x = 9.0909...
99x = 9
x = 9/99 = 1/11
```
- 0.0909... = 1/11

### Problem 7: convert 0.875 to a fraction

**Solution**

```
0.875/1 × 1000/1000 = 875/1000
GCF = 125
```
- 0.875 = 7/8

**Answers summary**
| Problem | Answer |
| --- | --- |
| 1 | 2/5 |
| 2 | 3/8 |
| 3 | 2/3 |
| 4 | 9/16 |
| 5 | 5/2 (2 1/2) |
| 6 | 1/11 |
| 7 | 7/8 |

## Common Mistakes (And How to Avoid Them)

**Eight mistakes and their fixes**
| Mistake | What goes wrong | Fix |
| --- | --- | --- |
| 1. Counting decimal places incorrectly | Thinking 0.125 has 2 decimal places | Count carefully: 0.125 has 3 decimal places, so the denominator is 1000 |
| 2. Not simplifying the fraction | Leaving 125/1000 instead of 1/8 | Always divide by the greatest common factor |
| 3. Multiplying only the numerator | Writing 0.125 = 125/1 | Multiply the numerator and the denominator by the same power of 10 |
| 4. Confusing terminating and repeating decimals | Using the terminating method on 0.333... | Use the algebra method for repeating decimals |
| 5. Not simplifying repeating-decimal fractions | Leaving 6/9 instead of 2/3 | Always simplify the final fraction |
| 6. Misplacing the decimal point | Turning 0.125 into 1250/1000 | Move the point exactly as many places as there are decimal digits |
| 7. Dropping the whole number | Writing 2.5 as 5/10 | 2.5 = 25/10 = 5/2, or 2 1/2 as a mixed number |
| 8. Not checking the answer | Assuming the conversion is correct | Divide the numerator by the denominator and compare with the original decimal |

Mistake 8 is the cheapest one to avoid. 7/8 is 7 ÷ 8 = 0.875, so the answer to problem 7 checks out in one division. If a check comes out slightly off, such as 0.3333 against 0.333..., that is rounding in the check, not an error in the fraction; [rounding rules: a complete guide](/blog/math/rounding-rules-complete-guide) explains where those small differences come from.

## Where to Go Next

Once your decimal is a fraction, you will usually do something with it. [Fraction operations: add, subtract, multiply, divide](/blog/math/fraction-operations-guide) walks through each operation with worked examples, and the [fraction calculator](/calculators/fraction-calculator) does the arithmetic and simplifies the result for you.

Decimal answers often come out of averages, too. When the mean of a set of scores is 86.6 or 12.5, [how to calculate an average step by step](/blog/math/how-to-calculate-an-average) shows where the decimal comes from, and this guide turns it into a fraction: 12.5 = 25/2 = 12 1/2.

## Frequently Asked Questions

**How do I convert a decimal to a fraction manually?**

Write the decimal as a fraction with denominator 1, multiply the numerator and denominator by 10 for each decimal place, then simplify by dividing both by their greatest common factor.

**How do I convert a repeating decimal to a fraction?**

Let x equal the decimal, multiply by 10 for each repeating digit, subtract the original equation so the repeating part cancels, and solve for x. Then simplify the fraction.

**What is the first step in converting a decimal to a fraction?**

Write the decimal as a fraction with denominator 1, for example 0.75 = 0.75/1.

**How do I simplify a fraction?**

Find the greatest common factor (GCF) of the numerator and denominator, then divide both by the GCF. 75/100 has a GCF of 25, so it simplifies to 3/4.

**What is 0.5 as a fraction?**

0.5 = 5/10 = 1/2.

**What is 0.25 as a fraction?**

0.25 = 25/100 = 1/4.

**What is 0.75 as a fraction?**

0.75 = 75/100 = 3/4.

**What is 0.125 as a fraction?**

0.125 = 125/1000 = 1/8.

**What is 0.333... as a fraction?**

0.333... = 3/9 = 1/3.

**What is 0.666... as a fraction?**

0.666... = 6/9 = 2/3.

**Can every decimal be converted to a fraction?**

Every terminating decimal and every repeating decimal can. Decimals that go on forever without repeating, such as π (3.14159...) or √2 (1.41421...), are irrational and cannot be written as an exact fraction of whole numbers. You can only approximate them, for example π ≈ 22/7.

**What is the difference between a terminating and a repeating decimal?**

A terminating decimal ends, like 0.125. A repeating decimal repeats a pattern of digits forever, like 0.333...

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