Convert Decimal To Mixed Number

Decimals are numbers that lie between integers on a number line. Decimals are another method to express fractions. 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 a numerical value that represents a part of a whole.

In this article, we have covered, Decimal definitions and Mixed Number definitions, Decimals To Mixed Numbers conversions and others in detail.

What are Decimals?

Decimals are a way to express numbers that fall between whole numbers, allowing for a more precise representation of quantities. They are a fundamental part of our numerical system and consist of a decimal point (.) followed by digits that can extend infinitely to the right.

Some examples of decimals are: 12.4, 1.89, -91.34, etc.

What are Mixed Numbers?

Mixed Numbers are also called Mixed Fractions, 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 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 definitions?

To convert a decimal to a mixed number, follow the steps added below:

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

Step 2: Remove 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.

Examples on Decimal To Mixed Number Conversion

Example 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.

Example 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}}

Example 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}}

Example 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

Example 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}}

Example 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}}