## What Is the Decimals To Fractions Conversion?

Decimals to fractions conversion refers to writing a given decimal in the form of a fraction. To convert decimals into fractions, we first need to identify the type of the decimal we are dealing with.

We can express the following decimals as fractions.

- Terminating decimals
- Repeating decimals

Terminating decimals | Decimals that have an end-digit.Examples: 7.5, 1.222, 9.64 |

Recurring/Repeating decimals | Non-terminating decimals in which a digit or a group of digits repeat themselves after the decimal point.Examples: 0.555…, 1.232323… |

Note that the non-terminating and non-recurring decimals cannot be expressed as fractions.

How do you convert decimals to fractions quickly? You can use this online Decimal to Fraction Converter to convert a given decimal into a fraction instantly without any calculation.

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## How to Use the Decimal to Fraction Converter

(Ensure that the conversion is assigned from “Decimal” to “Fraction.”)

**Step 1:** Substitute the value of the decimal in the numeric entry box labeled “Enter decimal.”

**Step 2: **Click on “Convert.”

The fraction result section shows the fraction form of the given decimal along with the calculation.

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## How to Convert Decimal to Fraction

In this section, we will discuss how to convert a terminating decimal into a fraction. Let’s understand the steps with the help of an example.

**Convert 0.75 into a fraction.**

**Step 1:** Write the decimal number in the form $\frac{Decimal}{1}$.

Here, $0.75 = \frac{0.75}{1}$

**Step 2:** Multiply both the numerator and denominator by the power of 10 corresponding to the number of digits after the decimal point. If the number of digits after the decimal point is 2, multiply both numerator and denominator by 100. The purpose here is to make the numerator a whole number.

Here, $\frac{0.75\times 100}{1 \times 100} = \frac{75}{100}$

**Step 3:** Simplify the resulting fraction.

$\frac{75 \div 25}{100 \div 25} = \frac{3}{4}$

**A Trick to Remember: **

There’s no specific decimal-to-fraction formula for conversion. However, we can simplify the steps into a simple trick.

- Remove the decimal point.
- Divide the resulting number by the power of 10 equal to the number of decimal digits.
- Simplify.

Examples:

- 9.5 as a fraction $= \frac{95}{10} = \frac{19}{2}$
- 2.25 as a fraction $= \frac{225}{100} = \frac{9}{4}$
- 0.124 as a fraction $= \frac{124}{1000} = \frac{312}{50}$

## Converting Repeating Decimals to Fractions

Let’s understand the steps to convert a repeating decimal to a fraction with the help of an example.

**Convert 0.2525… to a fraction**.

**Step 1: **Identify the repeating digits and the number of repeating digits in the given decimal number.

Repeating digits $= 25$

Number of repeating digits$ = 2$

**Step 2: Equate the decimal number to any variable. **** **

Let $x = 0.2525$ … ____(1)

**Step 3: **First ensure that only the repeating digits come after the decimal point. (*You can move the decimal point by multiplying the decimal by a suitable power of 10*). Then multiply both the sides of the equation by a power of ten equal to the number of repeating digits.

$x = 0.2525$ …

$100 x = 100 \times 0.2525$ …

$100 x = 25.25$ … ____(2)

**Step 4:** Subtract equation (1) from (2) and simplify.

$100x\;-\;x = 25.25$ …$-0.2525$ ….

$99x = 25$

$x = \frac{25}{99}$

## Converting Decimals to Mixed Fractions

Mixed numbers or mixed fractions consist of a whole number and a proper fraction.

**Examples: **$7\frac{1}{2},\; 3\frac{3}{4}$

Mixed numbers are always greater than 1. Thus, decimals that are greater than 1 can be written as mixed numbers. Let’s understand the steps to convert a decimal to a mixed fraction with an example.

**Convert 10.5 into a mixed fraction.**

**Step 1:** Split the decimal into its whole number part and the decimal part.

$10.5 = 10 + 0.5$

Whole number part: 10

Decimal part: 0.5

**Step 2:** Convert the decimal part into fraction.

$\frac{0.5}{1} = \frac{5}{10} = \frac{1}{2}$

**Step 3: **Write the whole number part with the fraction obtained in step 2.

$10.5 = 10\frac{1}{2}$

## Converting Negative Decimals to Fractions

To convert a negative decimal to a fraction, we first consider the decimal without the negative sign and follow the conversion steps that we discussed previously. Finally, attach the negative sign to the final answer.

**Example: Convert the decimal ****-9.3**** into a fraction.**

$9.3 = \frac{93}{10}$

Thus, $-9.3 = \;-\;\frac{93}{10}$

## Decimal to Fraction Conversion Table

Decimal | Fractional | Simplest form |
---|---|---|

0.1 | $\frac{1}{10}$ | $\frac{1}{10}$ |

0.2 | $\frac{2}{10}$ | $\frac{1}{5}$ |

0.3 | $\frac{3}{10}$ | $\frac{3}{10}$ |

0.4 | $\frac{4}{10}$ | $\frac{2}{5}$ |

0.5 | $\frac{5}{10}$ | $\frac{1}{2}$ |

0.75 | $\frac{75}{100}$ | $\frac{3}{4}$ |

0.125 | $\frac{125}{1000}$ | $\frac{1}{8}$ |

1.25 | $\frac{125}{100}$ | $\frac{5}{4}$ |

## Conclusion

In this article, we learned about decimals to fractions conversion with respect to terminating decimals and repeating decimals. Let’s solve a few examples and practice problems based on the same.

## Solved Examples on Decimal to Fraction Conversion

**1. Convert 0.125 to fractional form.**

**Solution:**

$0.125 = \frac{0.125}{1}$

The terminating decimal 0.125 has three digits after the decimal point. Multiply the numerator and denominator by 1000.

$\frac{0.125}{1} = \frac{0.125\times 1000}{1 \times 1000} \frac{125}{1000} = \frac{25}{200} = \frac{1}{8}$

Hence, $0.125 = \frac{1}{8}$

**2. Convert 8.75 to a fraction.**

**Solution:**

$8.75 = \frac{875}{100}$

$= \frac{175}{20}$ …dividing both numerator and denominator by 5

$= \frac{35}{4}$ …dividing both numerator and denominator by 5

Hence, $8.75 = \frac{35}{4}$

**3. Convert 4.5555… to a fraction.**

**Solution:**

4.555… is a repeating decimal with one repeating digit (5).

x=4.555… …(1)

Multiplu (1) by $10^1 = 10$ since only 1 digit is repeating.

$10x = 45.555$ … …(2)

Subtracting (1) from (2), we get

10x\;-\;x = 45.555$…$-4.555$…

$9x = 41$

$x = \frac{41}{9}$

Thus, 4.5555… $= \frac{41}{9}$

**4. Convert 10.75 to a mixed fraction.**

**Solution:**

$10.75 = 10 + 0.75$

Whole number part $= 10$

Decimal part $= 0.75$

Convert 0.75 into a fraction.

$0.75 = \frac{75}{100} = 34$

Thus, 10.75 as a mixed fraction $= 10\frac{3}{4}$

## Practice Problems on Decimal to Fraction Conversion

## Convert Decimal to Fraction: Definition with Examples

### Convert 0.375 to a fraction.

$0.375 = \frac{375}{1000} = \frac{3}{8}$

### Convert 6.125 to a mixed fraction.

$6.125 = 6 + 0.125$

Here, $\frac{125}{1000} = \frac{1}{8}$

Thus, $6.125 = 6\frac{1}{8}$

### Convert 3.25 to a mixed fraction.

$3.25 = 3 + 0.25$

$0.25 = \frac{25}{100} = \frac{1}{4}$

Hence, $3.25 = 3\frac{1}{4}$

### 0.007 $=$

$0.007 = \frac{7}{1000}$

## Frequently Asked Questions on Decimals to Fractions Conversion

**Can you convert a non-terminating, non-repeating decimal into a fraction?**

No, such decimals cannot be converted into fractions. They are irrational numbers.

**How can we find a decimal from a fraction?**

To convert a fraction into a decimal, divide the numerator by the denominator using the long division method. The quotient obtained as a result represents the required decimal value.

**What is a mixed recurring decimal?**

A decimal in which at least one of the digits after the decimal point is non-repeated and some digits are repeated is known as a **mixed recurring decimal**.

Example: 1.34666…

**Can every fraction be written as a decimal number?**

Yes, each fraction can be written as a decimal number. You just have to divide the numerator by the denominator.