Decimal Fraction Conversion
Easily convert decimal values into fractions or mixed numbers. For repeating decimals, simply enter the number of digits in the repeating sequence to get an accurate fractional result.
Decimal Fraction Conversion
Output
0
½
1
Introduction
What is a Decimal?
In mathematics, a decimal is a number that uses a decimal point to separate the whole number part from the fractional part. The dot itself is called the decimal point. The digits to the right of the decimal point represent values less than one (such as tenths, hundredths, etc.), allowing for precise calculations beyond whole integers.
What is a Fraction?
A fraction represents a part of a whole. It consists of two specific numbers separated by a line:
- Numerator (Top Number): Represents the number of parts you have.
- Denominator (Bottom Number): Represents the total number of equal parts that make up the whole.
How to Convert a Decimal to a Fraction
Follow these simple steps to convert any decimal into a fraction:
- Create a Basic Fraction: Write the decimal number as the numerator (top) and 1 as the denominator (bottom).
- Example: For 0.75, write 0.75 / 1.
- Remove the Decimal Point: Count how many digits are to the right of the decimal point. Multiply both the numerator and the denominator by 10 for every digit.
- Example: 0.75 has 2 digits. Multiply by 100 ().
- Result: 75 / 100.
- Simplify the Fraction: Find the Greatest Common Divisor (GCD) for both numbers and reduce the fraction to its lowest terms.
- Example: The GCD of 75 and 100 is 25.
- Final Result: 3/4.
- Mixed Numbers: If the decimal is greater than 1 (e.g., 1.5), convert the result into a mixed number if necessary.
Decimal to Fraction Conversion Table
| Decimal | Fraction | Decimal | Fraction |
|---|---|---|---|
| 0.0001 | 1/10000 | 0.5 | 1/2 |
| 0.001 | 1/1000 | 0.555... | 5/9 |
| 0.01 | 1/100 | 0.5714 | 4/7 |
| 0.0833 | 1/12 | 0.6 | 3/5 |
| 0.0909 | 1/11 | 0.625 | 5/8 |
| 0.1 | 1/10 | 0.666... | 2/3 |
| 0.111... | 1/9 | 0.7 | 7/10 |
| 0.125 | 1/8 | 0.7142 | 5/7 |
| 0.1428 | 1/7 | 0.75 | 3/4 |
| 0.166... | 1/6 | 0.777... | 7/9 |
| 0.2 | 1/5 | 0.8 | 4/5 |
| 0.222... | 2/9 | 0.833... | 5/6 |
| 0.25 | 1/4 | 0.8571 | 6/7 |
| 0.2857 | 2/7 | 0.875 | 7/8 |
| 0.3 | 3/10 | 0.888... | 8/9 |
| 0.333... | 1/3 | 0.9 | 9/10 |
| 0.375 | 3/8 | 1.1 | 11/10 |
| 0.4 | 2/5 | 1.25 | 5/4 |
| 0.4285 | 3/7 | 1.5 | 3/2 |
| 0.444... | 4/9 | 1.75 | 7/4 |
FAQ
What are the 3 types of decimals?
Terminating decimals end after a finite number of digits. Recurring decimals have one or more digits that repeat infinitely, such as 0.333... . Non-terminating and non-repeating decimals, also called irrational numbers, go on forever without a repeating pattern and cannot be written as a fraction.
What is a non decimal number?
A non-decimal number uses a number system based on something other than ten. The count of digits used in a numeral system is called its radix. For raw binary information, non-decimal numbers, particularly hexadecimal, are much easier to work with and are widely used by programmers, from the largest mainframe to the smallest microcomputer.
Where is a decimal?
The decimal point sits between the ones place and the tenths place. The whole number is written to the left of the decimal point, and the fractional part is written to the right. This placement makes a decimal number easy to read.
What are the 3 types of fraction?
The three main types of fractions are proper fractions, improper fractions, and mixed fractions. A fraction consists of a numerator and a denominator.
How do you do fractions in math?
Step 1: Make sure the bottom numbers (the denominators) are the same. Step 2: Add the top numbers (the numerators) and put that answer over the denominator. Step 3: Simplify the fraction if needed.
What is the formula of fraction?
A fraction represents the number of parts out of a total. The general formula is fraction = number of parts / total parts. Every fraction has a numerator showing the number of parts you have and a denominator showing the total number of equal parts in a whole.
What is a proper fraction?
A proper fraction is a fraction whose numerator is less than its denominator, meaning the value is less than one.
How do I turn a decimal into a fraction?
To convert a decimal to a fraction, place the decimal number over its place value. For example, in 0.6, the 6 is in the tenths place, so write 6 over 10 to get the equivalent fraction 6/10. Then simplify if possible.
What is improper fraction example?
An improper fraction has a numerator that is greater than or equal to the denominator. Examples include 5/3 and 9/8.
What are the most common fractions?
A common fraction is a fraction in which both the numerator and the denominator are whole numbers. For example, 1/2 and 3/4 are common fractions, while 1.2/4 is not because the numerator is not an integer.
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