Tool Overview

This tool converts a decimal number into a fraction. It shows the numerator and denominator, simplifies the fraction to lowest terms, and can show a mixed number when the value is greater than one. You can see how the conversion is done step by step and check the result by converting the fraction back to a decimal.

Decimals and fractions both represent parts of a whole. When the same value is needed in other forms, converting decimals to binary or to hexadecimal uses different methods. In school, recipes, or design you often need a fraction instead of a decimal. Doing the conversion by hand is slow and easy to get wrong, especially for repeating decimals like 0.333... This tool does the work for you and keeps the fraction in its simplest form.

The tool is for students, teachers, cooks, and anyone who needs to turn a decimal into a fraction. You enter one decimal at a time and get the fraction, mixed number if needed, and optional steps. No special math level is required. If you know what a decimal and a fraction are, you can use it. A calculator that performs the same conversion is available for different workflows.

Background & Concept Explanation

A decimal is a number written with a decimal point, like 0.75 or 1.5. The digits after the point show tenths, hundredths, thousandths, and so on. A fraction is a number written as one integer over another, like 3/4. The top number is the numerator and the bottom is the denominator. Both can represent the same value.

Some decimals stop after a few digits. These are called terminating decimals. For example 0.75 is three quarters and 0.125 is one eighth. Others repeat forever, like 0.333... where the 3 repeats. You can write repeating decimals in shorthand: 0.(3) or 0.333... Both mean the same thing. The tool accepts both styles.

To convert a terminating decimal to a fraction you count the decimal places, put the number over a power of 10, then simplify. For 0.75 you get 75/100, then divide top and bottom by 25 to get 3/4. For repeating decimals you use a different rule: the repeating part goes over a number made of nines. The tool does both and then simplifies so the numerator and denominator have no common factor except 1.

When the numerator is larger than the denominator the fraction is improper. The tool can show it as a mixed number: a whole number plus a proper fraction. For example 3/2 becomes 1 1/2. That makes it easier to read and use in real life.

Key Features

• Decimal input. You type a decimal in a single field. You can use a normal decimal like 0.75 or 1.5, or a repeating decimal like 0.333... or 0.1(6). The tool accepts a minus sign for negative numbers and treats a comma as a decimal point. This lets you enter values the way you see them in books or on screens.
• Fraction result in lowest terms. The tool shows the fraction as numerator over denominator and simplifies it using the greatest common divisor. You always get the smallest whole numbers that represent the same value. This is what you need for answers and for further calculation.
• Mixed number for improper fractions. When the numerator is greater than the denominator the tool also shows a mixed number: whole number plus fraction. You can copy either the fraction or the mixed form. This helps when you need to read or write amounts in everyday form.
• Decimal back. The tool shows the decimal you get when you divide the simplified numerator by the denominator. You can compare it to your original input to confirm the conversion is correct.
• Step-by-step derivation. You can expand a section to see the conversion steps. For terminating decimals you see how the decimal is turned into a fraction and then simplified. For repeating decimals you see how the repeating part is identified and the formula applied. This helps you learn or check the method.
• Repeating decimal support. You can enter repeating decimals as 0.333... or 0.1(6). The tool detects the repeating part and converts correctly. It marks the result as a repeating decimal so you know the original had a repeating pattern.
• Copy fraction, mixed number, and LaTeX. You can copy the simplified fraction, the mixed number if it exists, or the LaTeX code for the fraction. That helps when you paste into documents, worksheets, or math software.
• Sample decimals. Buttons let you quickly try common decimals such as 0.75, 0.5, 0.25, 0.333..., 0.1(6), 0.125, 1.5, and 2.25. This is useful when you are learning or when you need a standard example.
• Optional real-world context. You can ask for a short explanation of where the fraction is used in real life. The answer is generated by a backend service and is optional. It requires network access.

Common Use Cases

Homework and exams. A student has a decimal answer and must give the answer as a fraction in lowest terms. They enter the decimal, get the fraction and mixed number if needed, and can check the steps to understand the method.

Recipes and measurements. A recipe or design spec gives a decimal like 0.75 or 1.25. The user converts to a fraction to measure in cups or inches, e.g. 3/4 or 1 1/4. The mixed number form is easier to use on a ruler or measuring cup.

Teaching. A teacher shows how decimals relate to fractions. They enter 0.75, show the result 3/4, then open the steps to explain simplification. They can use 0.333... to show repeating decimals and the 0.1(6) form for more advanced notation.

Checking work. Someone has converted a decimal to a fraction by hand. They enter the original decimal here and compare the result. The decimal-back value and the steps help them verify their answer.

Documents and LaTeX. A report or worksheet needs a fraction in text or in LaTeX. The user converts the decimal once, then copies the fraction or the LaTeX code and pastes it into the document.

How to Use This Tool (Step-by-Step)

1. Open the tool. You will see an input field and sample decimal buttons.
2. Enter a decimal. Type a number such as 0.75, 1.5, or 0.333... You can use 0.1(6) for 0.1666... or 0.333... for repeating threes. Use a minus sign if the number is negative. You can use a comma instead of a period as the decimal point.
3. Or click a sample. Use the sample buttons to fill the input with common decimals like 0.75 or 0.333... Then you can edit the value if you want.
4. View the result. Below the input you will see the fraction as numerator over denominator in lowest terms. You will also see the decimal back value to verify.
5. Check the mixed number if it appears. When the value is greater than one you will see a mixed number (whole number plus fraction). Copy it if you need that form.
6. Copy what you need. Use the copy buttons to copy the fraction, the mixed number, or the LaTeX code.
7. Open the derivation steps if you want. Click the Derivation Steps section to expand it. Read the steps to see how the decimal was converted and simplified.
8. Use real-world context if you want. Click Get Insights to request a short explanation of where the fraction is used. Wait for the text. This step is optional and needs the network.
9. To start over, click Reset. The input returns to 0.75 and the result and steps are cleared.

Calculations & Logic

For a terminating decimal the tool counts how many digits are after the decimal point. The number is written as that integer over 10 raised to that count. For example 0.75 has two decimal places, so it becomes 75/100. Then the tool finds the greatest common divisor of the numerator and denominator and divides both by it to get the fraction in lowest terms. Here 75 and 100 share 25, so the result is 3/4.

For a repeating decimal in the form 0.1(6) the tool splits the value into a non-repeating part and a repeating part. It builds a fraction using a standard formula: the numerator is (the number formed by the whole part, non-repeating digits, and one copy of the repeating block) minus (the number formed by the whole part and non-repeating digits). The denominator is a number made of nines for each repeating digit and zeros for each non-repeating digit after the point. The result is then simplified to lowest terms.

For a repeating decimal written with an ellipsis like 0.333... the tool treats the last digit as the repeating part and the rest as non-repeating. The same style of formula is used. The number of nines and zeros in the denominator depends on the lengths of these parts.

The greatest common divisor is found with the Euclidean algorithm: repeatedly replace the larger number by the remainder when divided by the smaller until one number is zero; the other is the GCD. This is used only to simplify. The tool does not change the value of the fraction, only its form.

The mixed number is computed only when the absolute value of the numerator is greater than the denominator. The whole part is the quotient (with the correct sign) and the new numerator is the remainder. The denominator of the fraction part stays the same.

The decimal back value is computed by dividing the simplified numerator by the denominator. The result is rounded to a limited number of decimal places so it can be shown clearly. It is used only to verify the fraction matches the original decimal. Converting in the opposite direction—from binary to decimal or from hexadecimal to decimal—uses different algorithms.

Tips, Limitations & Best Practices

Use the notation the tool expects. For repeating decimals use 0.333... or 0.1(6). Do not type an infinite number of digits. If you type a long string of digits the tool may treat it as terminating and give an approximate fraction; use the repeating notation for exact results.

Input length and decimal places are limited. Very long decimals or very long repeating blocks may be rejected or truncated to avoid overflow. For most school and everyday use the limits are enough.

Negative numbers are supported. Type a minus sign in front of the decimal. The fraction and mixed number will be negative where applicable.

The tool converts one decimal at a time. If you have a list of decimals convert each one separately. There is no batch mode.

The optional real-world context is generated by a backend service. It needs network access and may be subject to usage limits. If it fails you still have the fraction and steps. The conversion does not depend on it.

When you copy LaTeX, paste it into a LaTeX editor or a tool that supports LaTeX. The format is \frac{numerator}{denominator}. You may need to adjust for your document if it uses a different macro.