Table of Contents
Converting decimals to fractions is a common mathematical task that can be simplified with the help of a decimal to fraction converter. This tool streamlines the process, making it easier to work with and understand decimal numbers in fraction form. If you don’t have access to online tools for converting decimals to fractions, you can manually convert them by understanding the place value of the decimal and writing it as a fraction. This involves placing the decimal number over its position value to create a fraction.
Decimal
Decimal is a base-10 numeral system used to represent numbers using ten digits: 0 to 9. In the decimal system, each digit’s position represents a power of 10, starting from the rightmost position with 10^0, then 10^1, 10^2, 10^3, and so on.
Fraction
A fraction represents a part of a whole and is written as one number (the numerator) divided by another number (the denominator), separated by a horizontal line.
How to Convert Decimal into Fractions?
To convert a decimal to a fraction, follow these steps:
- Step 1: Identify the decimal value.
- Step 2: Count the number of decimal places in the decimal value.
- Step 3: Remove the decimal point by multiplying the decimal value by 10^(number of decimal places). This will give you an equivalent fraction with the same value as the original decimal but without the decimal point.
- Step 4: Simplify the fraction, if possible, to its lowest terms.
Example:
Let’s convert the decimal 0.75 to a fraction.
- Step 1: The decimal value is 0.75.
- Step 2: There are two decimal places in 0.75.
- Step 3: Multiply 0.75 by 10^2 (since there are two decimal places), which is 100. So, 0.75 * 100 = 75.
- Step 4: The fraction is 75/100.
- Step 5: Simplify the fraction. Both the numerator and denominator can be divided by 25. So, 75/100 simplifies to 3/4.
The decimal 0.75 is equivalent to the fraction 3/4.
Also Read: Binary to octal converter
Decimal to Fraction Conversion Table
| Decimal | Fraction |
| 0.00001 | 1/100000 |
| 0.0001 | 1/10000 |
| 0.001 | 1/1000 |
| 0.01 | 1/100 |
| 0.08333333 | 1/12 |
| 0.09090909 | 1/11 |
| 0.1 | 1/10 |
| 0.11111111 | 1/9 |
| 0.125 | 1/8 |
| 0.14285714 | 1/7 |
| 0.16666667 | 1/6 |
| 0.2 | 1/5 |
| 0.22222222 | 2/9 |
| 0.25 | 1/4 |
| 0.28571429 | 2/7 |
| 0.3 | 3/10 |
| 0.33333333 | 1/3 |
| 0.375 | 3/8 |
| 0.4 | 2/5 |
| 0.42857143 | 3/7 |
| 0.44444444 | 4/9 |
| 0.5 | 1/2 |
| 0.55555555 | 5/9 |
| 0.57142858 | 4/7 |
| 0.6 | 3/5 |
| 0.625 | 5/8 |
| 0.66666667 | 2/3 |
| 0.7 | 7/10 |
| 0.71428571 | 5/7 |
| 0.75 | 3/4 |
| 0.77777778 | 7/9 |
| 0.8 | 4/5 |
| 0.83333333 | 5/6 |
| 0.85714286 | 6/7 |
| 0.875 | 7/8 |
| 0.88888889 | 8/9 |
| 0.9 | 9/10 |
| 1.1 | 11/10 |
| 1.2 | 6/5 |
| 1.25 | 5/4 |
| 1.3 | 13/10 |
| 1.4 | 7/5 |
| 1.5 | 3/2 |
| 1.6 | 8/5 |
| 1.7 | 17/10 |
| 1.75 | 7/4 |
| 1.8 | 9/5 |
| 1.9 | 19/10 |
| 2.5 | 5/2 |
Repeating Decimal to Fraction
Converting a repeating decimal to a fraction is a useful skill in mathematics. Repeating decimals are decimal numbers that do not terminate after a finite number of digits, and instead have one or more digits that repeat infinitely.
How to Convert Repeating Decimal to Fraction?
The process of converting a repeating decimal to a fraction involves the following steps:
- Identify the repeating digits in the given decimal number.
- Set the decimal number equal to a variable, such as x.
- Multiply both sides of the equation by a power of 10 such that the decimal point moves to the right of the repeating digits.
- Subtract the original equation from the new equation.
- Solve for the variable to obtain the fraction.
Example 1:
For example, to convert 0.7 repeating to a fraction:
Let x = 0.7777…
10x = 7.7777…
9x = 7
x = 7/9
Therefore, 0.7 repeating is equivalent to the fraction 7/9.
Example 2:
Convert 0.125125125… to a fraction.
Let x = 0.125125125…
1000x = 125.125125…
999x = 125
x = 125/999
So, 0.125125125… = 125/999.
By following these steps, you can convert any repeating decimal to its equivalent fraction form.
FAQs on Decimal to Fraction Converter
How do I convert a decimal to a fraction?
Identify the decimal value. Write down the decimal as a numerator. Determine the denominator based on the number of decimal places: a. If the decimal has one digit after the decimal point, use 10 as the denominator. b. If the decimal has two digits after the decimal point, use 100 as the denominator. c. For three digits after the decimal point, use 1000 as the denominator, and so on. Simplify the fraction, if possible.
How do you turn 0.75 into a fraction?
To convert 0.75 into a fraction: The decimal value is 0.75. The numerator is 75 (since there are two digits after the decimal point). The denominator is 100 (since there are two decimal places). The fraction is 75/100, which can be simplified to 3/4.
How do you convert 1.75 into a fraction?
To convert 1.75 into a fraction: The decimal value is 1.75. The numerator is 175 (since there are two digits after the decimal point). The denominator is 100 (since there are two decimal places). The fraction is 175/100, which can be simplified to 7/4.
What is 1.4 as a fraction?
To convert 1.4 into a fraction: The decimal value is 1.4. The numerator is 14 (since there is one digit after the decimal point). The denominator is 10 (since there is one decimal place). The fraction is 14/10, which can be simplified to 7/5.
What is 5.3 as a fraction?
To convert 5.3 into a fraction: The decimal value is 5.3. The numerator is 53 (since there is one digit after the decimal point). The denominator is 10 (since there is one decimal place). The fraction is 53/10.
What is 2.5 as a fraction?
To convert 2.5 into a fraction: The decimal value is 2.5. The numerator is 25 (since there is one digit after the decimal point). The denominator is 10 (since there is one decimal place). The fraction is 25/10, which can be simplified to 5/2.
