Education Journalist | Study Abroad Lead
Decimal and Fractions are both rational numbers, however, they both are different from each other. Fraction is the division of two numbers. Fractions are represented in two parts; the upper part is called the numerator and the lower part is called the denominator. On the other hand, a decimal number is also separated into two parts separated by a decimal point; the digits which are on the left side are the whole number whereas the number on the right side represent the fractional part. The conversion of decimals to fractions is one of the most commonly carried out steps in Arithmetic. With the help of strong division basics, one can easily convert decimals to fractions, as well as fractions to decimals.
| Table of Content |
Key Terms: Decimals, Fractions, Mixed Fractions, Recurring Decimal, Negative Decimals, Conversion, Simplest Form, Numerator, Denominator, Terminating Decimals
Also read: Isosceles Triangle Theorems
What are Decimals?
[Click Here for Sample Questions]
The number which comes in between integers and non-integers is called a decimal number. The dot represent in between numbers is called the decimal point. For Example, 34.5 is a decimal number. Here, 34 represent the whole number and 5 is the fractional part.
There are two types of decimal numbers basically,
- Recurring Decimal Numbers- The repeating and non-terminating decimals are called Recurring Decimal Numbers.
- Non-Recurring Decimal Numbers- The non-repeating and terminating decimals are called Non-Recurring Decimal Numbers.
Decimals
Read More: Difference Between Fraction and Rational Numbers
What are Fractions?
[Click Here for Sample Questions]
The number is expressed as a quotient, in which there is a numerator and denominator. A fraction has two parts; the upper part is called Numerator and the lower part is called the Denominator.
The types of fractions are elaborated below:
- Unit Fraction- Fraction which has 1 as a numerator is called a unit fraction.
- Proper Fraction- Fractions in which the numerator is less than the denominator is called proper fraction.
- Improper Fraction- Fraction in which numerator is more than dominator is called Improper Fraction.
- Mixed Fraction- Mixed fractions consist of a whole number along with a proper fraction.
Types of Fraction
Read More: How to Rationalize the Denominator?
How To Convert Decimals Into Fractions?
[Click Here for Sample Questions]
To convert a decimal into a fraction we need to follow three simple steps:
- Step 1: First, write the Decimal number without the Decimal point in the numerator.
- Step 2: Count the numbers after the decimal point to the right side and put that many zeroes in the Denominator.
- Step 3: Then reduce the fraction in simplest form
For Example: Let us convert 30.5 into fractions.
- Step 1: Write the decimal number without a decimal point in the numerator which means 30.5 will be written as 305.
- Step 2: Since there is one number after the decimal, the denominator will be 10.
- Step 3: The fraction obtained now needs to be reduced in the simplest form as follows
30.5 = \(\frac{305}{10}\) = \(\frac{6}{12}\)
Conversion of Decimals to Fractions
Read More: Addition and Subtraction of Integers
Conversion of Repeating Decimals to Fractions
Repeating Decimals, also known as Recurring Decimals, are those decimal numbers that do not end after a finite number of decimal places and keep on repeating in the number.
In order to convert repeating decimals to fractions, here is an example to understand the procedure.
Let us convert 0.77777... to a fraction.
Let x = recurring number, 0.77777..
Let n= the number of recurring digits, i.e. 7
Now, Multiply the recurring decimal number by 10, i.e.,
10 x = 10 x 0.77777 = 7.77777...
This means that
10x - x =7
9x = 7
∴ x= 7/9
Read More: Decimal Expansion of Rational Numbers
Conversion of Decimals to Mixed Number Fractions
Decimals that have values greater than 1 can be converted and written as mixed fractions. Here are the steps to convert decimal numbers into mixed fractions:
- Step 1: Firstly, we have to consider the whole number part and decimal part of the decimal number separately.
- Step 2: Write the decimal number without a decimal point in the numerator and count the numbers after the decimal point to the right side and put that many zeroes in the Denominator.
- Step 3: Now, the next step is to simplify the fraction obtained.
- Step 4: Lat step involves attaching the whole number part of the original number with the fraction obtained after simplification.
Mixed Fractions
Let's Convert 2.5 into a mixed fraction.
Consider 2 and 0.5 separately.
Now, 0.5 can be written as 5/10 in fractional form.
Simplify the fraction as
5/10 = 1/2
Last step is to attach the whole number to the simplified fraction as given below:
2+1/2= 2\(\frac{1}{2}\)
Read More: Multiplicative Inverse
Conversion of Negative Decimal to a Fraction
Given below are the steps to convert any negative decimal number to a fraction:
- Step 1: First, remove the negative sign from the decimal number.
- Step 2: Now, you have to do the conversion of decimals to fractions as explained in the above steps.
- Step 3: Put the negative sign to the fraction obtained.
Let us convert -3.2 into a fraction.
First, we will remove the negative sign and will consider it as 3.2
As there is only one digit after the decimal, the fraction would be 32/10.
Convert 32/10 to its simplest form, i.e,
32/10 = 16/5
Now, apply a negative sign to the fraction.
16/5 = -16/5
Read More: Irrational Numbers
Things to Remember
- Decimal and fractions are both different from each other. Decimal and fraction are both Rational numbers.
- The number which comes in between integers and non-integers is called a decimal number. There are two types of decimal numbers- Recurring and non-recurring.
- A fraction has two parts; the upper part is called Numerator and the lower part is called the Denominator. The types of fractions are- unit, proper, improper and mixed fraction.
- In order to convert decimals to fractions, we have to write the Decimal number without the Decimal point in the numerator.
- The next step is to count the numbers after the decimal point to the right side and put that many zeroes in the Denominator.
- Lastly, we have to reduce the fraction in the simplest form.
- The same process of conversion is followed for negative decimals too.
Read More: Minors and Cofactors
Solved Examples
Ques. Convert 0.5 into Fraction. (3 Marks)
Ans. To convert decimal into fraction,
First, we will write the decimal number without a point, i.e, 0.5 will be written as 5.
Since there is one number after the decimal, the denominator will be 10.
0.5 = \(\frac{5}{10}\)
Now, we will simplify the fraction as
0.5 = \(\frac{5}{10}\) = \(\frac{1}{2}\)
Ques. Convert 0.75 into Fraction. (2 Marks)
Ans. Write the number without a decimal point and then count the number of zeroes after the point and put that many zeroes in the denominator and simplify the fraction.
0.75= \(\frac{75}{100}\) = \(\frac{3}{4}\)
Ques. Convert -3.2 into fractions. (3 Marks)
Ans. Since this is a negative decimal, so first we will write the number without the negative sign.
-3.2 = 3.2
Now, write the number without a decimal point and put the number of digits after decimal in the denominator as zeroes. -3.2 = 3.2 = \(\frac{32}{10}\)
Write the fraction in its simplest form as the last step.
-3.2 = 3.2 = \(\frac{32}{10}\) = \(\frac{16}{5}\) =-\(\frac{16}{5}\)
Ques. Convert 4.75 into a fraction. (3 Marks)
Ans. To convert 4.75 into fractions,
Step 1: 4.75 will be as 475.
Step 2: Since there are two numbers after the decimal, the denominator will be 100.
4.75 = \(\frac{475}{100}\)
Step 3: Simplify the fraction as
4.75 = \(\frac{475}{100}\) = \(\frac{19}{4}\)
Ques. Convert 0.625 into a fraction. (3 Marks)
Ans. To convert 0.625 into a fraction,
Step 1: 0.625 will be as 625.
Step 2: Since there are three numbers after the decimal, the denominator will be 1000.
0.625 = \(\frac{625}{1000}\)
Step 3: Simplify the fraction as
0.625 = \(\frac{625}{1000}\) = \(\frac{25}{40}\) =\(\frac{5}{8}\).
Ques. Convert 0.333 into a fraction. (3 Marks)
Ans. To convert 0.333 into a fraction,
Step 1: 0.333 will be as 333.
Step 2: Since there are three numbers after the decimal, the denominator will be 1000.
0.333 = \(\frac{333}{1000} \)
Step 3: Since the fraction cannot be simplified, the fraction will be as
0.333 = \(\frac{333}{1000} \)
Ques. Convert 0.35 into a fraction. (3 Marks)
Ans. To convert 0.35 into a fraction,
Step 1: 0.35 will be as 35.
Step 2: Since there are two numbers after the decimal, the denominator will be 100.
0.35= \(\frac{35}{100}\)
Step 3: Simplify the fraction as
0.35= \(\frac{35}{100}\) =\(\frac{7}{20}\).
Ques. Convert 4.75 infractions and also convert them into mixed fractions. (3 Marks)
Ans. To convert 4.75 into a mixed fraction,
Step 1: 4.75 will be as 475.
Step 2: Since there are two numbers after the decimal, the denominator will be 100.
4.75= \(\frac{475}{100}\)
Step 3: Simplify the fraction as
4.75= \(\frac{475}{100}\) =\(\frac{19}{4}\)
Step 4: In mixed fractions, it would be written as 434
Ques. Convert 0.225 into a fraction. (3 Marks)
Ans. To convert 0.225 into a fraction,
Step 1: 0.225will be as 225.
Step 2: Since there are three numbers after the decimal, the denominator will be 1000.
0.225= \(\frac{225}{1000}\)
Step 3: Simplify the fraction as
0.225= \(\frac{225}{1000}\) =\(\frac{9}{40}\).
Ques. Convert 0.0035 in the simplest fraction. (3 Marks)
Ans. To convert 0.0035 in the simplest fraction,
Step 1: 0.0035 will be as 35.
Step 2: Since there are four numbers after the decimal, the denominator will be 10000.
0.0035= \(\frac{35}{10000}\)
Step 3: Simplify the fraction as
0.0035= \(\frac{35}{10000}\) =\(\frac{7}{2000}\).
Comments