Are you looking for help on how to convert a decimal fraction to a fraction number? Don’t Fret as you will find easy methods to convert from decimal to fraction here. Before, diving let’s learn about Decimals, Fractions Definitions. To Convert a Decimal to a Fraction place the decimal number over its place value. For better understanding, we even listed Solved Problems on Decimal Fraction to Fraction Number Conversions here. You can easily convert from decimals to fractions and no calculators are needed.
Decimal Definition
Decimal Numbers are the Numbers that have base 10 in Computer Science. However, in Mathematics Decimal Number is a number that has a decimal point in between digits. In Other Words, we can say that decimals are fractions that have denominator 10 or multiples of 10.
Example: 2.35, 6.78, 8.79 are decimals
Fraction Definition
A fraction is a part of a whole number and is represented as a ratio of two numbers a/b in which a, b are integers and b≠0. The two numbers are namely numerator and denominator. There are different types of fractions namely proper, improper, mixed fractions. we can perform all basic operations on the fractions.
Example: \(\frac { 1 }{ 3 } \), \(\frac { 3 }{ 4 } \) are fractions
How to Convert a Decimal to Fraction?
Learn the Steps to Convert Decimal to Fraction here. Follow the below-listed procedure to change between Decimals to Fractions easily. They are in the following fashion
- Firstly, write the fraction with the decimal number as the numerator and with 1 in the denominator.
- Remove the decimal places by multiplication. Firstly, count how many places are there right to the decimal. Let Suppose there are x places then you need to multiply both the numerator and denominator with 10x
- Reduce the fraction to the lowest form by dividing both the numerator and denominator of the fraction with GCF.
Steps to Convert a Repeating Decimal to Fraction
Converting a regular Decimal to Fraction is an easy method. But, converting a recurring or repeating decimal fraction is a bit tedious and can be confusing. Let us learn how to convert a repeating decimal to a fraction by considering few examples.
Step 1: Let us assume the decimal number as X
Step 2: Count the number of trailing or repeating digits. If there are x digits multiply with 10x and consider it as the 2nd equation.
Step 3: Subtract Equation (1) from (2) and Solve for X
Step 4: Reduce the obtained fraction to the lowest form by dividing both the numerator and denominator with their GCF. The obtained fraction is the converted value of the repeating decimal given.
Decimal to Fraction Table
Below is the list of decimal values converted to fractions that you might find useful during your calculations. They are in the following fashion
| Decimal | Fraction | Decimal | Fraction |
| 0.5 | \(\frac { 1 }{ 2 } \) | 1.5 | \(\frac { 6 }{ 4 } \) |
| 0.25 | \(\frac { 1 }{ 4 } \) | 0.857142… | \(\frac { 6 }{ 7 } \) |
| 0.6666… | \(\frac { 2 }{ 3 } \) | 0.875 | \(\frac { 7 }{ 8 } \) |
| 0.4 | \(\frac { 2 }{ 5 } \) | 1.4 | \(\frac { 7 }{ 5 } \) |
| 0.285714… | \(\frac { 2 }{ 7 } \) | 3.333… | \(\frac { 10 }{ 3 } \) |
| 0.2222 | \(\frac { 2 }{ 9 } \) | 1.42857… | \(\frac { 10 }{ 7 } \) |
| 0.75 | \(\frac { 3 }{ 4 } \) | 1.875 | \(\frac { 15 }{ 8 } \) |
| 0.428571… | \(\frac { 3 }{ 7 } \) | 0.9375 | \(\frac { 15 }{ 16 } \) |
| 2.5 | \(\frac { 5 }{ 2 } \) | 0.95454… | \(\frac { 21}{ 22 } \) |
| 0.83333 | \(\frac { 5 }{ 6 } \) | 0.78125 | \(\frac { 25 }{ 32 } \) |
Decimal to Fraction Conversion Examples
1. Convert 2.25 to fraction?
Solution:
Step 1: To change 2.25 to fraction firstly write the numerator part with a decimal number leaving the denominator part with 1.
Step 2: Count the number of decimal places to the right of the decimal point. Since give decimal value has 2 digits next to the decimal point multiply with 102 both the numerator and denominator.
= \(\frac { (2.25*100) }{ (1*100) } \)
= \(\frac { 225 }{ 100 } \)
Step 3: Reduce the obtained fraction in the earlier step to its lowest form by dividing them with GCF. GCF(225, 100) = 25
i.e. \(\frac { 225÷25 }{ 100÷25 } \)
= \(\frac { 9 }{ 4 } \)
Therefore, 2.25 converted to fraction form is \(\frac { 9 }{ 4 } \)
2. Convert 101.1 to fraction?
Solution:
Given Decimal value is 101.1
Step 1: Place the given decimal value in the numerator of the fraction and place 1 in the denominator.
Step 2: Count the number of digits after the decimal point. Since the given decimal value has only 1 digit multiply both the numerator and denominator with 10. i.e. \(\frac { 101.1*10 }{ 1*10 } \) = \(\frac { 1011 }{ 10 } \)
Step 3: The above fraction can’t be reduced further since the GCF is 1.
Therefore, 2.25 converted to fraction form is \(\frac {1011 }{ 10 } \)
FAQs on Decimal to Fraction
1. What is a Decimal?
Decima Number is defined as a number whose whole number part and fraction part is separated by a decimal point(dot).
2. What are the types of Decimals?
There are two different types of Decimals
- Terminating Decimals or Non-Recurring Decimals
- Non-Terminating or Recurring Decimals
3. What is a Fraction?
A fraction is a numerical value that is a part of a whole. It is evaluated by dividing a whole into a number of parts.
4. How do I Convert a Decimal to a Fraction?
To Convert a Decimal to a Fraction, place the decimal number over its place value.