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Convert Decimal To Mixed Number

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  • Last Updated : 27 May, 2022
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Decimals are numbers that lie between integers on a number line. In mathematics, they are just another method to express fractions. We may write more accurate values of quantifiable things such as length, weight, distance, money, and so on using decimals. The numbers to the left of the decimal point are integers or whole numbers, while the numbers to the right are decimal fractions. If we proceed right from one place, the following place will be (1/10) times smaller, resulting in a (1/10)th or tenth place value. Example: 0.50, 10.20, 25.6, etc., are some examples of Decimals form. Fractions are defined as numerical value that represents a part of a whole. A fraction is a portion or section of any amount taken from the total, which might be any number, a specified value, or an item. A fraction is also known as a portion or section of a larger quantity. It is represented by the ‘/’ sign, as in a/b. 

For instance, 3/4 is a fraction in which the upper section, which is 3, represents the numerator, and the bottom part, which is 4, represents the denominator.

Mixed Fraction or Mixed Number 

A mixed fraction is a form of the fraction that has both a whole number and a fractional part. A mixed fraction is defined as a fraction formed by combining a whole number and a fraction. A mixed fraction is one that is expressed by its quotient and remainder. For example:  3{\Large\frac{1}{2}}  is a mixed fraction in which 3 is the quotient and 1 is the remainder. A mixed fraction is, therefore, the product of a whole number and a proper fraction.

How to convert Decimal To Mixed Numbers?

Solution:

To convert a decimal to a mixed number, perform these steps:

  • Step 1: Determine how many decimal places are in the given number.
  • Step 2: Remove the decimal point from the number and divide it by a power of ten equal to the number of decimal places. So, if there are two decimal places, we must divide the number by 102, which is 100. To put it another way, the number of zeros should be equal to the number of decimal places.
  • Step 3: Simplify the fraction and, if necessary, convert it to a mixed number if it is an improper fraction.

Sample Questions

Question 1: Convert 7.5 into a mixed fraction?

Solution: 

To convert a decimal to a mixed number, perform these steps:

Step 1: Determine how many decimal places are in the given number.

Step 2: Remove the decimal point from the number and divide it by a power of ten equal to the number of decimal places. So, if there are two decimal places, we must divide the number by 102, which is 100. To put it another way, the number of zeros should be equal to the number of decimal places. Take away the decimal point, Rewrite in fraction form,

7.5 = 75/10

Step 3: Simplify the fraction and, if necessary, convert it to a mixed number if it is an improper fraction.

Thus, 7.5 = 75/10

= 15/2 

Now convert it into mixed number,

= 15/2 

 By simplifying, 

 

Here, we simplify 15/2 in a mixed fraction 7 1/2, here 7 is quotient and 1 remainder.

Therefore, 7.5 = 15/2 =  7{\Large\frac{1}{2}}  in a mixed fraction.

Question 2: Convert 3.25 into a mixed fraction?

Solution: 

We will use steps to convert decimal to fraction.

Step 1: Determine the place value of the digits after the decimal in the number, if there are 1 digit after decimal then divide it by 10 and two digits divide by 100 and so on.

Step 2: Use it to figure out what the fraction’s denominator is 100

Step 3: Take away the decimal point. Rewrite it in fraction form, then simplify it

Numerator/Denominator = 325/100

Step 4: Express it in terms of the smallest Simplest Fraction: 325/100

Thus, 3.25 = 325/100

= 65/20

= 13/4 is an improper fraction.

Therefore , convert 13/4 in to mixed fraction,

13/4 =  4{\Large\frac{1}{3}}

So, 3.25 in mixed fraction will be 4{\Large\frac{1}{3}}

Question 3: Convert 42.56 into a mixed fraction?

Solution: 

We will use steps to convert decimal to fraction,

Step 1: Determine the place value of the digits after the decimal in the number , if there are 1 digit after decimal then divide it by 10 and two digits divide by 100 and so on 

Step 2: Use it to figure out what the fraction’s denominator is 100

Step 3: Take away the decimal point. Rewrite it in fraction form, then simplify it

Numerator/Denominator = 4256/100

Step 4: Express it in terms of the smallest Simplest Fraction: 4256/100

Thus, 42.56 = 4256/100

= 2128/50

= 1064/25

= 42{\Large\frac{14}{25}}

Question 4: Convert 0.25 into a Mixed fraction?

Solution: 

We will use steps to convert decimal to fraction .

Step 1: Determine the place value of the digits after the decimal in the number, if there are 1 digit after decimal then divide it byb 10 and two digits divide by 100 and so on.

Step 2: Use it to figure out what the fraction’s denominator is 100.

Step 3: Take away the decimal point. Rewrite it in fraction form, then simplify it.

Numerator/Denominator = 25/100

Step 4: Express it in terms of the smallest Simplest Fraction: 25/100

Thus, 0.25 = 25/100

= 1/4

Question 5: Convert 9.745 into a mixed fraction?

Solution: 

We will use steps to convert decimal to fraction.

Step 1: Determine the place value of the digits after the decimal in the number , if there are 1 digit after decimal then divide it by 10 and two digits divide by 100 and so on.

Step 2: Use it to figure out what the fraction’s denominator is 1000.

Step 3: Take away the decimal point. Rewrite it in fraction form, then simplify it.

Numerator/Denominator = 9745/100

Step 4: Express it in terms of the smallest Simplest Fraction: 9745/1000

Thus, 9.745 = 9745/1000

= 1949/200

Now convert into mixed fraction 

Therefore, 9.745 = 1949/200 =  9{\Large\frac{149}{200}}

Question 6: Convert 2.98 into a mixed fraction?

Solution: 

We will use steps to convert decimal to fraction.

Step 1: Determine the place value of the digits after the decimal in the number, if there are 1 digit after decimal then divide it by 10 and two digits divide by 100 and so on.

Step 2: Use it to figure out what the fraction’s denominator is 100.

Step 3: Take away the decimal point. Rewrite it in fraction form, then simplify it.

Numerator/Denominator = 298/100

Step 4: Express it in terms of the smallest Simplest Fraction : 298/100

Thus, 2.98 = 298/100

= 149/25 

Here its an improper fraction , now , convert it into mixed fraction :

= 149/25              

So, 2.98 = 149/25 =  5{\Large\frac{24}{25}}


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