Converting decimals to fractions is one of the most commonly performed steps in arithmetic. But to do that, you need to have your departmental basics. Once you understand this, you will be able to convert decimals to fractions as well as fractions to decimals.

Check out the table from decimals to fractions in this lesson to get a better idea of how to convert decimals to fractions.

1. | How do I convert decimals to fractions? |

2. | Decimal to fraction conversion table |

3. | Convert decimal to fraction: inches |

4. | Frequently asked questions about converting decimals to fractions |

## How do I convert decimals to fractions?

Here is a simple 4-step process to convert anyDecimalin afraction.

### Steps to convert:

**Step 1**- Identify the place value of the decimal places in the number.**step 2**- Use that to determine what the denominator of the fraction would be.**Step 3-**Remove the decimal point. Rewrite and simplify the fraction form.**step 4**- Express in terms of the lowest equivalent fraction.

Let's see an example to understand these steps.

**Example:**Convert 0.5 to a fraction.

**Solution:**Let's apply the steps we've learned.

Step 1: Identify the place value of the last digit.

0.5 <------------ 5 is in tenth place. (0.5 means 0.50)

Step 2: The denominator would be 10

Step 3: Fraction format: numerator/denominator = 5/10

Step 4: Simplest Shape: 1/2

Also 0,5=5/10=1/2.

Go through the following sections for more examples of converting fractions to decimals. There are three unique cases that you might come across when converting decimals to fractions and they are listed below:

- Convert repeating decimals to fractions
- Convert decimals to mixed fractions
- Convert a negative decimal to a fraction

Let's get acquainted with each case in detail.

### Convert repeating decimals to fractions

Repeating decimal numbers are those that do not end after a finite number of decimal places, and some specific digits or a single digit after the decimal point are repeated over and over in the number. To convert a repeating decimal to a fraction, a specific method must be used. Let's look at an example to understand this.

Convert 0.77777... to a fraction.

Let x = repeating number, i.e.

0,77777 ....

n= the number of repeating digits, i.e. 7

Multiply the repeating decimal number by 10, i.e.

10x=7,77777...

This implies

10x - x=7

9x=7

∴x= 7/9

### Convert decimals to mixed fractions

Decimal numbers with values greater than 1 can be written as mixed fractions. Check out the steps to convert such decimals to mixed fraction form:

**Step 1**- Consider separately the integer part and the decimal part in the given decimal.**step 2**- Write the decimal part in fraction form by ignoring the decimal point and dividing it by a power of 10 that has the same number of zeros as the decimal places.**step 3**- Simplify the obtained fraction.**step 4**- Join the integer part of the original number with the fraction obtained in step 3. That would be your answer.

Let's consider an example.

Convert 2.5 to a mixed fraction.

- Step 1: Consider 2 and 0.5 as separate units.
- Step 2: 0.5 can be written as 5/10 (as a fraction).
- Step 3: 5/10 = 1/2 (in simplified form).
- Step 4: 2+1/2= \(2\dfrac{1}{2}\)

∴ 2.5 can be written as a fraction as \(2\dfrac{1}{2}\).

### Convert a negative decimal to a fraction

To convert a negative decimal to a fraction, let's do the following:

**Step 1**: Remove the minus sign from the decimal number.**step 2**: Perform the conversion for the positive value.**step 3**: Apply the negative sign to the fractional answer.

For example, convert -3.2 to a fraction.

- Step 1: Remove the negative sign. Think of it as 3.2
- Step 2: After the fraction comes a digit, so multiply and divide 3.2 by 10.
- Step 3: Convert 32/10 to its lowest form and apply a negative sign to the fractional answer.

So the answer is -16/5.

## Decimal to fraction conversion table

The following decimal to fraction conversion table shows some commonly used fractions and their decimal equivalents.

Decimal | Bruchäquivalent | fracture in its simplest form |
---|---|---|

0,1 | 1/10 | 1/10 |

0,2 | 2/10 | 1/5 |

0,3 | 3/10 | 3/10 |

0,4 | 4/10 | 2/5 |

0,5 | 5/10 | 1/2 |

0,6 | 6/10 | 3/5 |

0,75 | 75/100 | 3/4 |

0,125 | 125/1000 | 1/8 |

0,625 | 625/1000 | 5/8 |

1.25 | 125/100=\(1\dfrac{25}{100}\) | \(1\dfrac{3}{4}\)=7/4 |

This is the tabular representation of the conversion of a decimal number to its fraction equivalent. Now look at the diagram below and understand it visually.

## Convert decimal to fraction: inches

Decimal and fractions are used to represent inch values. To convert a specific inch measurement from decimals to fractions, we need to focus on the fractional part of the decimal. For example, if we need to convert 6.25 inches to its fractional equivalent, it has 6 in the integer part and 0.25 in the fractional part. 0.25 has two decimal places, so it can be written as 25/100 as a fraction, which can be reduced to 1/4. Therefore we get 6.25 = 6 1/4 inches. Here's how we convert inches from decimals to fractions.

decimal inch | fraction of an inch |
---|---|

36.000 | 36" |

36.125 | 36 1/8" |

36.250 | 36 1/4" |

36.375 | 36 3/8" |

36.500 | 36 1/2" |

36.625 | 36 5/8" |

36.750 | 36 3/4" |

### Process to convert decimals to fractions of inches

A fractional inch such as 36.125 inches includes 3 feet and an additional 0.125 inches. There are three decimal places. Therefore, multiply and divide 0.125 by 1000. For 0.125, the best option is 1/8 inch. Therefore the height is \( 3\dfrac{1}{8} \)" in.

**Points to remember:**

Procedure for converting decimals to fractions:

- Identify the place value of the last digit in the number.
- Use that to determine what the denominator of the fraction would be.
- Remove the decimal point. Rewrite and simplify the fraction form.
- Express in terms of the lowest equivalent fraction.

**☛Related Article**

Check out some more interesting articles on converting decimals to fractions.

- fraction to decimal
- Fraction to Decimal Chart
- Decimal to fractional calculator

## Frequently asked questions about converting decimals to fractions

### What is decimal to fraction conversion?

Converting decimals to fractions is a method of writing decimal values as fractional values and vice versa. To convert the number from decimal to fractional form, we divide the number by the power of 10, so the number of zeros should be equal to the number of decimal places in the given number, and simplify the fraction. Example: decimal form = 7.5 = 75/10 = 15/2 (fraction of 7.5).

### How do I convert decimals to fractions?

To convert a decimal to a fraction, we follow these three basic steps:

- Rewrite the number ignoring the decimal point.
- Divide the number by the place value of the last digit in the fractional part of the number.
- Simplify the fraction.

### How do you convert fractions to decimals?

To convert any fraction to decimal form, we just need to divide its numerator by its denominator.

### What is the difference between a fraction and a decimal?

The main difference between fraction and decimal is that fraction represents a ratio between two while decimal can be used for writing infinite values and for more precision.

### How do you convert mixed fractions to decimals?

To convert a mixed fraction to a decimal, we must first convert it to an improper fraction. Then we can divide the numerator by the denominator to convert it to a decimal.

### What is the use of Decimal Fraction Chart?

When we represent the decimal value in a fraction form (p/q), we use decimal fraction charts for easy and quick calculations. It also helps with reverse conversion, which also converts fractions to decimals.

**☛ Check now for more practice:**

- Decimal to fractional calculator
- Fraction to decimal calculator
- Converting decimals to fraction worksheets

### How do you write 0.25 decimal as a fraction?

Let's see how to convert 0.25 to fractions step by step:

- Step 1: Count the numbers after the decimal point.
- Step 2: There are two decimal places. Therefore, multiply and divide 0.25 by 100.
- Step 3: Simplify 25/100 to its lowest form, which is 1/4.

So 1/4 is the fractional form of 0.25.

### What are repeating and non-repeating decimals?

Repeating decimal numbers are those in which one or more digits are repeated over and over, e.g. 2 = 0.5.

### How are decimals and fractions represented?

Fractions are written in the form of p/q, where q≠0, while decimal numbers have the integer and fractional parts connected by a decimal point, for example 0.5.

## FAQs

### Which method is used to change a fraction to a decimal? ›

To convert a fraction to a decimal, we'll just **divide the numerator...by the denominator**. In our example, we'll divide 1 by 4. 1 divided by 4 equals 0. To keep dividing, we'll add a decimal point and a zero after the 1.

**What is the fastest way to convert fraction to decimal? ›**

The easiest way to convert a fraction to a decimal is to **divide the numerator (the top of the fraction) by the denominator (the bottom of the fraction) by using a calculator**. The resulting answer will be the value of the fraction expressed as a decimal number.

**How do you turn 10.5 into a fraction? ›**

Solution: 10.5 as a fraction is **21/2**.

**What is 2.5 as a fraction? ›**

2.5 can be represented as a fraction in numerous ways. The most common way is **2 1/2**, which means two and a half. This can also be written as 2.5 or 25/10. Another way to represent 2.5 as a fraction is 5/2, which means five halves.

**What is the first step in converting a decimal to a fraction? ›**

**How to Convert Decimals to Fractions**

- Write the decimal divided by one. For example, say you're given the decimal . ...
- Next, you want to multiply both the top and bottom of your new fraction by 10 for every digit to the left of the decimal point. ...
- The final step is reducing the fraction to its simplest form.

**What are the methods for converting fractions decimals and percents? ›**

**To change a fraction to a decimal, divide the numerator by the denominator**. To change a fraction to a percent, • Change the fraction to a decimal. Change the decimal to a percent. Or, move the decimal point 2 places to the left.

**How many methods are used to convert decimal fraction to binary? ›**

However, there are **two direct methods** are available for converting a decimal number into binary number: Performing Short Division by Two with Remainder (for integer part), Performing Short Multiplication by Two with result (For fractional part) and Descending Powers of Two and Subtraction.

**How do you turn 0.123123 into a fraction? ›**

0.123123… = **123/999** (since 123 is the repeating part of the decimal and it contains 3 digits). We can divide both the top and bottom parts by 3 to find that 0.123123… = 123/999 = 41/333.

**How do I convert to fractions? ›**

Decimals can be written in fraction form. To convert a decimal to a fraction, **place the decimal number over its place value**. For example, in 0.6, the six is in the tenths place, so we place 6 over 10 to create the equivalent fraction, 6/10.

**What is 5.8 as a fraction? ›**

Solution: 5.8 as a fraction is **29/5**.

### What is 9.5 as a fraction? ›

Solution: 9.5 as a fraction is **19/2**.

**How do you turn 6.5 into a fraction? ›**

Solution: 6.5 as a fraction is **13/2**.

**What is .40625 as a fraction? ›**

Solution: 0.40625 as a fraction is 13/32.

**What is 3.6 as a fraction? ›**

Solution: 3.6 as a fraction is **18/5**.

**How do you turn 3.14 into a fraction? ›**

Solution: 3.14 as a fraction is **157/50**.

**What is 5.375 as a fraction in simplest form? ›**

Solution: 5.375 as a fraction is **43/8**.

**What is 15.375 as a fraction? ›**

Solution: 15.375 as a fraction is **123/8**.

**What is 2.75 1.25 4.75 3.80 as a fraction? ›**

Expert-Verified Answer

Answer: The correct answer is **2 9/20**.

**What is 2.65 as a fraction in simplest form? ›**

Solution: 2.65 as a fraction is **53/20**.

**What is 2.36 as a fraction in simplest form? ›**

Solution: 2.36 as a fraction is **59/25**.

### How do you turn 3.2 into a fraction? ›

Solution: 3.2 as a fraction is **16/5**.

**What is the last step when converting a decimal to a fraction? ›**

Step 1- Identify the place value of the digits after the decimal, in the number. Step 2- Use that to determine what the denominator of the fraction would be. Step 3- **Remove the decimal point**. Re-write in the fraction form and simplify it.

**What is the easiest method to convert decimal to binary? ›**

**How to convert a decimal to binary using division**

- Divide the decimal number by 2. First, divide the original number by 2. ...
- Take the whole number from your result and note the remainder. After dividing 61 by 2, the whole number left over after the equation is 30. ...
- Write the remainders you receive in order from last to first.

**What are the two methods of converting between binary and decimal numbers? ›**

There are mainly two methods to convert a binary number into decimal number − **using positional notation, and using doubling**.

**How do I convert a decimal to a mixed fraction? ›**

To convert a decimal to a mixed number, find the place value of the decimal part. The decimal part becomes the numerator of the faction and the place value is the denominator. Write the whole number, then make a fraction from the decimal part by placing the decimal part over the place value.

**How do you convert 16.67 to a fraction? ›**

...

Percent to Fraction Table.

Percent | Fraction |
---|---|

16.67 % | 1 6 |

20 % | 1 5 |

22.22 % | 2 9 |

25 % | 1 4 |

**When converting a decimal to a fraction what becomes the denominator? ›**

To convert a decimal to a fraction, we write the decimal number as a numerator, and we write **its place value** as the denominator.

**How do you turn 0.245 into a fraction? ›**

Solution: 0.245 as a fraction is **49/200**.

**How do you convert 0.324 to a fraction? ›**

Solution: 0.324 as a fraction is **81/250**.

**What is 0.345 as a fraction? ›**

Solution: 0.345 as a fraction is **69/200**.

### What's 2.625 as a fraction? ›

Solution: 2.625 as a fraction is **21/8**.

**What is 1.50 as a fraction? ›**

Solution: 1.50 as a fraction is **3/2**.

**What is 1.25 as a fraction? ›**

Solution: 1.25 as a fraction is **5/4**.

**What is 0.33333 as a fraction? ›**

So we can see that our original decimal of 0.333333... is equal to the fraction 1/3. Let's summarize the steps to follow to convert any repeating decimal to a fraction. (a) Identify the repeating part in the decimal. Then set the decimal equal to a variable.

**What is 0.105 as a fraction? ›**

Solution: 0.105 as a fraction is **21/200**.

**What is 0.15 as a fraction? ›**

Solution: 0.15 as a fraction is **3/20**.

**How do you turn 0.025 into a fraction? ›**

Solution: 0.025 as a fraction is **1/40**.