One of the most common arithmetic operations is converting decimals to fractions. However, you must first master the fundamentals of division. Moreover, you’ll be able to convert decimals to fractions and fractions to decimals after you understand this.

However, to convert a decimal to a fraction, we must first write the decimal in fraction form by adding a denominator of 1. To eliminate the decimal (.) from the given number, multiply both the numerator and denominator by multiples of ten. Meanwhile, if the decimal number 1.9 is used, the equivalent fraction will be 17/10. We can’t just keep going with 17/10.

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**Decimal: **

However, decimal numbers are numbers with a base of ten in terms of computers. A decimal number, on the other hand, is a number with a dot (.) or decimal point between the digits in mathematics. However, fractions having denominators of 10 or multiples of 10 are known as decimals. Decimals include 8.96, 12.6, 75.1, 8.29, 7.765, and so on.

**Fraction: **

A fraction is a unit of measurement that is divided by a whole number. It’s written as a ratio of two numbers, a/b, where a and b are both integers, and b0 is also an integer. Meanwhile, the numerator and denominator are the two numbers. 2/3 is a portion of 2, 6/9 is a component of 6, and so on. Infractions, we can do any arithmetic operations. However, proper, Improper, and Mixed fractions are the three sorts of fractions.

**How to Convert Decimal to Fraction?**

Let’s have a look at how to convert decimals to fractions.

However, to begin, write the provided decimal as a ratio (p/q), with the denominator equal to 1.

For each decimal point, multiply the numerator and denominator by multiples of 10 until the decimal in the numerator becomes a whole number. Meanwhile, multiply by 100/100 if there are two numbers after the decimal point.

Simply put, the fraction that results.

With the help of a simple example, the following diagram illustrates how to convert decimal to fraction.

Hence, 0.20 = 0.20/1 = ( 0.20 × 100 ) / (1×100) = 20/100 = ⅕

**Converting Decimal to Fraction Exercises **

However, here you will find solutions to difficulties involving the conversion of decimal to fraction. We can also find solutions for converting fractions to decimals. This decimal to fraction conversion example, given below, will aid your grasp of the idea.

**Decimal to Fraction Sums**

**Question 1: **

However, we must find the fraction form of the number given the decimal value of 0.8.

We can also multiply multiple fractions together to find equivalent fractions.

8/10 = 0.8

Now divide 8/10 by 2 in both the numerator and denominator, yielding (8×2)/(10×2) = 16/20.

Let’s multiply 8/10 by 5 and 10 in both the numerator and denominator to obtain additional equivalent fractions.

40/50 = 4/5 = 8×5/10×5

Hence, 80/100 = 8×10/10×10

As a result, 0.8 decimal fractions are 8/10, 4/5, and 80/100.

**Question 2:**

Convert 5.25 into a fraction.

Solution: Given, 5.25is a decimal number.

Then, Multiply and divide 5.25 by 100.

Then, 5.25 × 100/100 = 525/100

However, If we simplify it more, we get;

21/4

Meanwhile, by multiplying the numerator and denominator by 2, we may determine the equivalent fractions.

For example,

21×2/4×2 = 42/8

So, 5.25 equivalent fractions are 525/100, 21/4 and 42/8.

**Question 3:**

2.25 is a fraction, thus converting it to a fraction.

Solution: Follow the steps outlined above:

2.25/1

Multiply 2.25/1 by 100 in the numerator and denominator because there are two numbers following the decimal point.

Then, (2.25/1) x (100/100) = 225/100 = 9/4

**Question 4:**

Make a mixed fraction out of 1.625.

Solution: 1.625 can be written as 1.625/1.

Then, remove up to three decimal places by multiplying by 1000.

Hence, 1.625/1 x (1000/1000) = 1625/1000

Similarly, simplifying 1625/1000 we get;

⇒ 13/8

However, now we’re going to convert it to a mixed fraction.

13/8 = 1 5/8

Hence, 1 5/8 is the mixed fraction equivalent to 1.625.

However, more examples of how to convert fractions to decimals can be found in the sections below. When converting a decimal to a fraction, you may encounter three different situations, which are listed below:

- Firstly, Converting Repeating Decimal to Fraction
- Then, Converting Decimals to Mixed Number Fractions
- Then, Convert Negative Decimal to a Fraction

However, let’s take a closer look at each scenario.

**Repeating Decimal to Fraction**

However, repeating decimals are ones in which certain digits or a single digit after the decimal point keep repeating in the number after a finite number of decimal places. Moreover, there is a specific method that must be used to convert any repeating decimal to a fraction. However, let’s look at an example to see what I mean.

To a fraction, convert 0.77777…

Let x represent a recurring number, such as 0.77777…. and n represent the number of recurring digits, such as 7.

Multiply the recurring decimal by ten, for example,

10x=7.77777…

This implies,

10x – x=7

Hence, 9x=7

∴ x= 7/9

**Converting Decimal to Fraction Mixed Number**

Mixed fractions can be written as decimals with values greater than one. Consider the following steps for converting decimal integers to mixed fractions:

**Step 1:**

Firstly, Separately consider the entire number and decimal parts of the supplied decimal number.

**2nd step:**

Then, convert the decimal part to fractional form by disregarding the decimal point and dividing by a power of ten with the same number of zeros as decimal places.

**Step 3:**

Similarly, simplify the obtained fraction.

**4th Step-**

Then, combine the whole number portion of the original number with the fraction found in step 3. That’d be your response.

**Consider the following scenario.**

Make a mixed fraction out of 3.5.

1st step:

Firstly, separate 3 and 0.5 into two parts.

2nd step:

Similarly, 0.5 can be written as 5/10 (as a fraction).

3rd step:

Hence, 5/10 = 1/2 (in the simplified form).

4th step:

3 + ½ = 3½

∴ Hence, 3.5 can be composed as 3½ as a fraction.

**Convert Negative Decimal to a Fraction**

However, follow the instructions below to convert any negative decimal value to a fraction:

1st step:

Firstly, remove the negative sign from the decimal number.

2nd Step:

Then, convert the positive value to a negative value.

3rd step:

Meanwhile, to get the fraction solution, add a negative sign.

**Convert – 5.2 to a fraction, for example.**

1st Step: Firstly, get rid of the minus symbol. Then, consider the number 5.2.

2nd Step: Because the fraction has one digit after it, multiply and divide 5.2 by 10 similarly.

3rd Step:

Then, reduce 52/10 to its simplest form and indicate the fraction with a negative sign.

**Convert Decimal to Fraction Inches**

Inches are represented using decimal and fractional numbers. However, we must concentrate on the fractional part of the decimal number to convert a given inch measurement from decimals to fractions. When converting 6.25 inches to fractional equivalents, for example, the whole number part is 6 and the fractional part is 0.25. Because 0.25 has two digits after the decimal point, it can be represented as 25/100, which can be reduced to 1/4 as a fraction. As a result, 6.25=6 1/4 inches is obtained. This is how we go from decimal to fractional inches. Read Also: What are Capital Resources?

However, converting Decimal to Fraction Inches is a simple operation.

A fractional inch figure, such as 36.125 inches, includes 3 feet plus 0.1inchesnch. However, after the decimal, there are three digits. As a result, divide and multiply 0.125 by 1000. The best option for 0.125 is 1/8 of an inch. As a result, the height will be 3⅛.

**Decimal to Fraction Formula**:

- Determine the place value of the number’s last digit.
- Then, use this to figure out what the fraction’s denominator will be.
- Then, remove the decimal point from the equation. Simplify it by rewriting it in fraction form.
- In terms of the smallest Equivalent fraction, express.

**Decimal to Fraction Example 1**

Convert 0.135 to a fraction using your knowledge of decimal to fraction conversion.

Solution:

Step 1: Firstly, determine the last digit’s place value. In the thousandth place, 0.135 4 is found.

2nd Step: Hence, 1000 would be the denominator.

Step 3: Fractional representation: 135/1000 (numerator/denominator)

4th Step: The Most Basic Form: 27/200.

∴ 0.135 = 27/200.

**Decimal to Fraction Example 2**

Silvia is a voracious reader. She picked up a new book to read. However, Silvia read 20 pages per day out of a total of 200 pages. How many pages did she read in a single day? Then, Calculate the decimal equivalent of the fraction.

Solution:

However, the number of pages in total = 200.

Then, pages read by her each day = 20.

Numbering of pages read by her per day = 20/200 = 1/10.

∴ She read 1/10 or 0.1 pages in a day.

**Decimal to Fraction Table**

Let’s take a look at some decimals represented as fractions, which are widely employed in mathematical calculations.

Decimal |
Fraction |

0.5 | 1/2 |

0.25 | 1/4 |

0.6666… | 2/3 |

0.4 | 2/5 |

0.285714… | 2/7 |

0.2222 | 2/9 |

0.75 | 3/4 |

0.428571… | 3/7 |

2.5 | 5/2 |

0.83333 | 5/6 |

**Decimal to Fraction Worksheet**

Simplify the given decimals by converting them to fractions.

Convert 9.25

(Answer: 37/4)

Convert 0.005

(Answer: 1/200)

Convert 10.010

(Answer: 1001/100)

Convert 99.95

(Answer: 1999/20 or 99 19/20)

Convert 0.42

(Answer: 21/50)

**Decimal to Fraction Questions**

What decimal of an hour is a second?

Ans. 0.00027

If 2994 ÷ 14.5 = 172, then 29.94 ÷ 1.45 =?

Ans. 17.2

When 0.232323….. is converted into a fraction, then the result is:

Ans. 23/99

The expression (11.98 x 11.98 + 11.98 x x + 0.02 x 0.02) will be a perfect square for x equal to:

Ans. 0.04

3889 + 12.952 – ? = 3854.002

Ans. 47.95

Every year, the price of commodity X rises by 40 paise, whereas the price of commodity Y rises by 15 paise. If the price of commodity X was Rs. 4.20 in 2001 and the price of commodity Y was Rs. 6.30 in 2001, in which year will commodity X cost 40 paise higher than commodity Y? Every year, the price of commodity X rises by 40 paise, whereas the price of commodity Y rises by 15 paise. If the price of commodity X was Rs. 4.20 in 2001 and the price of commodity Y was Rs. 6.30 in 2001, in which year will commodity X cost 40 paise higher than commodity Y?

Ans. 2011.

**Frequently Asked Questions**

### How do you turn a decimal number into a fraction?

By mentioning q=1, write the provided decimal number in the form p/q. Now divide and multiply the numerator and denominator by n decimal places. Simplify the fraction you’ve just calculated.

### How to write decimal into mixed fraction form?

Let’s pretend that 7.3 is a decimal number. 7.3/1 is the fraction form of the decimal.

The numerator and denominator should now be multiplied by ten.

(7.3/1) x (10/10) = 73/10

73 divided by 10 equals 7 and 3 the remaining.

As a result, 73/10 can be expressed in mixed fraction form as 7 3/10.

### What is 0.575 as a fraction?

(0.575/1) x (1000/1000)

= 575/1000

= 23/40

### What is 1.50 as a fraction?

1.50 is equivalent to 3/2 as a fraction.

### What is 0.5 as a fraction?

Write 0.5 as 0.5 /1

Multiply and divide by 100 to get;

50/100

Simplify to get ½.