Online Calculator Resource

# Decimal to Fraction Calculator

Decimal to Fraction

$2.625 = 2 \frac{5}{8}$Showing the work

Rewrite the decimal number as a fraction with 1 in the denominator$2.625 = \frac{2.625}{1}$Multiplying by 1 to eliminate 3 decimal places, we multiply top and bottom by 103 = 1000$\frac{2.625}{1}\times \frac{1000}{1000}= \frac{2625}{1000}$Find the Greatest Common Factor (GCF) of 2625 and 1000, if it exists, and reduce our fraction by dividing both numerator and denominator by it, GCF = 125,$\frac{2625 \div 125}{1000 \div 125}= \frac{21}{8}$Simplifying the improper fraction,$= 2 \frac{5}{8}$In conclusion,$2.625 = 2 \frac{5}{8}$

## Calculator Use

This calculator converts a decimal number or repeating decimal number to a fraction. If the decimal number is greater than one, the answer is presented as a mixed number: a whole number plus a fraction. If the decimal is less than one, the answer is presented as a simple fraction.

If you are converting a terminating decimal to a fraction, enter 0 for "How many decimal places repeat?" If you are converting a repeating decimal to a fraction, enter the number of decimal places that repeat.

## How to Convert Decimals to Fractions

When you change a decimal to a fraction you begin with either a terminating decimal or a repeating decimal.

Decimal Number
A number and a fraction of a number, represented by digits and including a decimal point.
Terminating Decimal
A decimal number with a finite number of digits. Commonly called a decimal number.
Repeating Decimal
A decimal number with a digit or a group of digits that repeat indefinitely. Also called a recurring decimal.

### How to convert a terminating decimal to a fraction

1. Rewrite the decimal number number as a fraction, with a denominator of 1.
2. Multiply to eliminate the decimal places. If you have X decimal places then multiply numerator and denominator by 10X. This is essentially the same as multiplying by 1.
3. Find the Greatest Common Factor (GCF) of the numerator and denominator, if it exists, and reduce the fraction by dividing both numerator and denominator by this GCF.
4. Finally, simplify the remaining fraction to a mixed number if possible.

#### Example

Convert 2.625 to a fraction.

1. Rewrite the decimal number number as a fraction (over 1)

$$2.625 = \dfrac{2.625}{1}$$

2. Multiplying by 1 to eliminate 3 decimal places, we multiply numerator and denominator by 103 = 1000

$$\dfrac{2.625}{1}\times \dfrac{1000}{1000}= \dfrac{2625}{1000}$$

3. Find the Greatest Common Factor (GCF) of 2625 and 1000, if it exists, and reduce the fraction by dividing both numerator and denominator by the GCF. Here, the GCF is 125.

$$\dfrac{2625 \div 125}{1000 \div 125}= \dfrac{21}{8}$$
$$= 2 \dfrac{5}{8}$$

In conclusion,

$$2.625 = 2 \dfrac{5}{8}$$

#### Decimal to Fraction

• For another example, convert 0.625 to a fraction.
• Multiply 0.625/1 by 1000/1000 to get 625/1000.
• Reducing we get 5/8.

To convert a terminating decimal to a fraction you can use a shortcut to express the decimal as a fraction then reduce the fraction.

• For example, convert 36.125 to a fraction
• Since 3 is in the ten's place, 6 is in the one's place, 1 is in the tenth's place, 2 is in the hundredth's place and 5 is in the thousandth's place we can say that 36.125 = (3*10)/1 + (6*1)/1 + (1/10) + (2/100) + (5/1000). In order to add these we need to find the common denominator which is 1000. So, 30000/1000 + 6000/1000 + 100/1000 + 20/1000 + 5/1000 = 36125/1000.
• The shortcut is to look at the number we want to convert as 36.125/1 then multiply top and bottom of this fraction by the value that will give us an integer in the numerator. In this case we multiply by 1000/1000. And since 1000/1000 = 1/1 = 1 we are only multiplying by 1 so the resulting fraction is equal to our original number with the decimal part.
• Finally, reduce the fraction to 36 1/8.

### Example of how to convert a repeating decimal to fraction

Convert 2.666 to a fraction.

Let X equal our decimal number
Equation 1:

$$X = 2.\overline{666}\tag{1}$$

Since we have 3 digits in the repeating decimal group, create a second equation by multiplying both sides by 103 = 1000 Equation 2:

$$1000 X = 2666.\overline{666}\tag{2}$$

Subtracting equation (1) from (2)

\eqalign{1000 X &= &\hfill2666.666...\cr X &= &\hfill2.666...\cr \hline 999X &= &2664\cr}

We get

$$999 X = 2664$$

Solving for X

$$X = \dfrac{2664}{999}$$

Find the Greatest Common Factor (GCF) of 2664 and 999, if it exists, and reduce the fraction by dividing both numerator and denominator by the GCF. Here the GCF is 333.

$$\dfrac{2664 \div 333}{999 \div 333}= \dfrac{8}{3}$$
$$= 2 \dfrac{2}{3}$$

In conclusion,

$$2.\overline{666} = 2 \dfrac{2}{3}$$

#### Repeating Decimal to Fraction

• For another example, convert 0.333 to a fraction.
• Create the first equation with X equal to the repeating decimal number
• X = 0.333 (1)
• Create the second equation by multiplying both sides of (1) by 1000
• 1000X = 333.333 (2)
• Subtract equation (1) from (2) to get 999X = 333 and solve for X
• X = 333/999
• Reducing we get X = 1/3
• Answer: X = 0.333 = 1/3

Wikipedia contributors. "Repeating Decimal," Wikipedia, The Free Encyclopedia. Last visited 18 July, 2016.

Cite this content, page or calculator as:

Furey, Edward "Decimal to Fraction Calculator"; from http://www.calculatorsoup.com - Online Calculator Resource.