Decimal to Fraction Calculator

One of the most basic mathematical practices is converting decimal numbers to fractions. It really helps one do calculations and even understand better. A Decimal-to-Fraction Calculator automates the conversion and will convert any decimal value into its equivalent fraction. Here’s a step-by-step procedure, for manual conversion of a decimal into a fraction.

How to Convert a Decimal to a Fraction?

The method to convert a decimal fraction into a fraction manually can be accomplished by:

Step 1: Set up a fraction with the decimal in the numerator (top number) and a 1 in the denominator (bottom number).
Step 2: Terminate the decimal by multiplying. Now, count how many places there are to the right of a decimal. Next, multiply numerator and denominator by 10^x, where x is the number of decimal places.
Step 3: Reduce the fraction. After that, find the Greatest Common Factor {GCF} of numerator and denominator and divide both numerator and denominator by GCF.
Step 4: If possible, reduce the remaining fraction into a mixed number fraction.

Example: Convert 1.354 to a Fraction

Starting with the decimal number:

The decimal is given to be 1.354.

Writing the decimal as a fraction:

Conversion to fraction: 1.354 / 1.

This will eliminate the decimal point when multiplying by 10ⁿ:

There are three digits after the decimal, so we multiply by 10³ (1000).

\frac{1.354 \times 1000}{1 \times 1000} = \frac{1354}{1000}

The GCF can be used to simplify the fraction by dividing by it:

The G.C.F of 1354 and 1000 is 2, so we will divide them both by 2.

\frac{1354 \div 2}{1000 \div 2} = \frac {677}{500}.

Convert the improper fraction to a mixed number whenever required:

Converting 677 / 500, an improper fraction, into a mixed number:

1 \frac{177}{500}.

This is how we can convert the decimal 1.354 to a fraction.

1 \frac{177}{500}.

Convert a Repeating Decimal to a Fraction

1. At first, create an equation such that x equals the decimal number.
2. Count the decimal places, y. Create a second equation multiplying both sides of the first by 10y.
3. After that, subtract the second equation from the first equation.
4. Next, solve for x
5. Utimately, reduce the net fraction.

Example: Convert repeating decimal 2.666 to a fraction

1. Write an equation whereby x is the decimal number
Equation 1:

x = 2.\overline{666}

2. Count the number of decimal places y. There are 3 digits in the repeating decimal group; thus, y = 3. Then multiply each side of the first equation by 10³ = 1000, creating the 2^nd Equation:

1000x = 2666.\overline{666}

3. Subtract equation (1) line from equation line (2):

\begin{array}{r} 1000x = 2666.666...\\x = 2.666...\\ \hline 999x=2664\end{array}

Thus,

999x=2664

4. Solve for x:

x= \frac{2664}{999}

5. Reduce the fraction. Find the Greatest Common Factor (GCF) of 2664 and 999 and reduce the fraction by dividing both the numerator and the denominator by GCF = 333.

\frac{2664 \div 333}{999 \div 333}= \frac{8}{3}

Now, simplify the improper fraction.

x= 2\frac{2}{3}

This is the result, what we get:

2.\overline{666}=2\frac{2}{3}

Benefits of Using a Decimal to Fraction Calculator

• An instantaneous and accurate conversion.
• Time-saving when it comes to very tricky decimals.
• Useful in any educational and professional set-up.
• Manual calculation errors all but eliminated.