Decimal Fraction

A fraction comprises a numerator and a denominator. In a decimal fraction, the fraction has a denominator that is a power of 10. The first thing to remember when we convert a decimal to a fraction is to express the denominator as a power of 10.  Also, the number of zeros in the power of 10 should be equal to the number of decimal places in the given number. In short, a decimal fraction will have a denominator of 10 or its powers, like 100, 1000, 10000, and so on.

For example, 

    0.5 = 5/10

    0.25 = 25/100

    0.75 = 75/100

These fractions all have denominators that are powers of 10 (10, 100, etc.).

Decimal fractions can be read in two ways: by naming each digit separately after the decimal point or by using place values. Understanding how to read them correctly helps in math and everyday life. 

Step 1: Read the whole number (if any) before the decimal point. For example, 3.125

Step 2: Say the word “point” when you reach the decimal (.).

Step 3: Read each digit, one by one, after the decimal point separately. For example, 3.125 can be read as “three point one two five”.  
 

Step 4: You can also read the decimal as a fraction by using place values. For example, 3.125 as “three and one hundred twenty-five thousandths”.

Basic mathematical operations are applicable on decimal fractions. All these operations are discussed in detail:

Addition of Decimal Fractions 

The addition of decimal fractions can be done in two ways. 

Convert decimal fractions to decimal form before adding.
 

Step 1: First, convert them into decimal form. 

For example, if we need to add 45/100 and 65/1000, 

• 45/100 = 0.45
• 65/1000 = 0.065
   

Step 2: Now, adding them together:

        0.45 + 0.065 = 0.515 
 

Step 3: To make it back to a fraction, look for how many decimal places are there. 
 

Here, there are three digits after the decimal point. So we use 1000 as the denominator. To convert 0.515 into a fraction, we need to multiply and divide it by 1000. 0.5151000  1000 = 515/1000

So the answer is 515/1000

Convert the given decimal fractions to like fractions before adding. 

Step 1: First, make both the fractions into like fractions. 

For example, 45/100 and 65/1000

For that, find the LCM of both denominators, 100 and 1000. 

The LCM is 1000

    
Step 2: Convert each fraction

45100  = 45  10100  10 = 4501000

651000 already has a denominator of 1000, so it remains the same. 

    
Step 3: Add them together 

 4501000 + 651000 = 5151000

 So the answer is 515/1000

Subtraction of Decimal Fractions

Similarly, to subtract decimal fractions, convert them into decimal form first. For example, if we subtract 65/1000 from 45/100.

45100 = 0.45

651000 = 0.065

Now, subtracting

 0.45 – 0.065 = 0.385

Convert back into fraction, 

0.3851000 × 1000 = 3851000

So the answer is 385/1000.

Multiplication of Decimal Fractions

While multiplying a decimal fraction by a power of 10, it is all about calculating the place of the decimal point as per the number of zeros in the power of 10. For example, 63.457 × 100 = 6345.7, here, the power of 10 is 102. We multiply it by 63.457, we count the number of zeros and shift the decimal point two places accordingly.

 

Division of Decimal Fractions

When we divide a decimal fraction by 10 or any power of 10, we move the decimal point to the left. We change the number of places by counting how many zeros there are in the power of 10 we divide. 

For example, 63.457  100 = 0.63457 
(since the denominator 100 (102) has two zeros, we move the decimal two places to the left. 
 

A number can be written as a decimal with a finite number of decimal places or a decimal with an infinite number of decimal places. Decimals can be classified into three types:
 

• Terminating Decimals
• Non-terminating Repeating Decimals
• Non-terminating Non-repeating Decimals
   

A decimal fraction can be represented as a decimal with a finite number of decimal places. The number of zeros in the power of 10 in the denominator determines the number of decimal places. Hence, decimal fractions can be considered as terminating decimals, but not all terminating decimals are decimal fractions unless their denominator can be expressed as a power of 10. 
 

To convert numbers into decimal fractions, different methods are used depending on whether the number is a fraction or a decimal or a mixed fraction. The methods are discussed below:
 

• Converting Fractions to Decimal Fractions
  
  Let’s take the example of the fraction 5/4.
  
  Step 1: First, find a number that, when multiplied by the denominator, results in 10 or a multiple of 10. 
  
  Step 2: In this case, multiplying 4 by 25 gives 100.
  
  Step 3: Multiply with the same number to the numerator and denominator.
   

        (5 x 25) / (4 x 25)  = 125/100

Thus, the decimal fraction of 5/4 is 125/100 or 1.25 

 

• Converting Mixed Numbers to Decimal Fractions
  
  Let’s take an example of 2 x (1/5)
  
  Step 1: First, we need to convert the mixed number, 2 (1/5) into an improper fraction.
  
  2 x (1/5) = 11/5
  
  Step 2: Next, to get a denominator of 10, we must multiply both the numerator and denominator by 2.
  
  (11 x 2)/ (5 x 2) = (22/10)
  
  Therefore, the decimal fraction of 2 x (1/5) is  22/10.  

• Converting Decimal Numbers to Decimal Fractions
  
  Let’s take an example of 6.2
  
  Step 1: Write the decimal number as a fraction with 1 in the denominator.
  
  6.2/1
  
  Step 2: Shift the decimal one place to the right and add a zero to the denominator.
  62.0/10
  
  Step 3: Now that the numerator is a whole number, we get the decimal fraction.
  
  6.2 = 62/10
  
  Thus, 6.2 as a decimal fraction is 62/10.

Decimal fraction is easy for calculation, just by shifting the decimal point, it ensures the precision and correctness of the number.

• Money and Finance: Prices, bills, and bank transactions involve decimals (e.g., $4.75, $99.99). Calculating discounts, interest rates, and taxes require decimal fractions. 
   
• Measurements in Daily Life: Length, weight, and volume are often measured in decimals (e.g., 2.5 kg, 1.75 liters). Cooking recipes use decimals for precise ingredient amounts. 
   
• Science and Medicine: Medication doses are measured in decimals (e.g., 2.5 mg of medicine). Scientific measurements use decimals for accuracy (e.g., temperature: 36.7° C).