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A fraction whose denominator is a power of 10 is known as a decimal fraction. Some of the examples of decimal fractions are 1/10, 4/10, 35/100, etc. Let us learn more about it in this article.
|1.||What is Decimal Fraction?|
|2.||Types of Decimal Fraction|
|3.||Decimal Fraction Conversions|
|4.||FAQs on Decimal Fraction|
What is Decimal Fraction?
A decimal fraction is defined as those fractions whose denominators are a power of 10, say 10, 100, 1000, 10000, and so on. Fraction is the relation between a part and a whole. So, in a decimal fraction, the whole is always divided into parts equal to a power of 10 like 10, 100, 1000, and so on. For example, 7/10 implies that we consider 7 parts out of a total of 10 parts. When we convert decimal to fraction, the first step is to write the denominator as a power of 10 in which the number of zeros will be equal to the number of decimal places in the given number. For example, 2.5 can be written as 25/10, so 25/10 is a decimal fraction. It is one of the types of fractions which can be used for decimal fraction conversions. Look at the image below to understand what are decimal fractions with the help of examples.
Now, let us understand operations on decimal fractions.
Addition of Decimal Fractions
By now, it must be clear to you that decimal fractions have 10, 100, 1000, and so on as their denominators. To add two or more decimal fractions, there are two ways which are given below:
- By converting decimal fractions to decimals and then add.
- By converting the given decimal fractions to like fractions, and then add.
By following the first method, we first convert decimal fractions to decimals and then add those values. For example, let us add 2/10 + 34/100. 2/10 can be written as 0.2, and 34/100 can be written as 0.34. Now, 0.2 + 0.34 = 0.54. Therefore, 2/10 + 34/100 = 0.54 which can be written as 54/100. Let us add the same numbers using the second method. To convert the given fractions (2/10 and 34/100) into like fractions, we find the LCM of the denominators. The least common multiple of 10 and 100 is 100. So, multiply the numerator and denominator of 2/10 by 10.
⇒ 2/10 = (2 × 10)/(10 × 10)
⇒ 2/10 = 20/100
Now, 20/100 + 34/100 = 54/100. Therefore, 2/10 + 34/100 = 54/100.
Subtraction of Decimal Fractions
Subtraction of decimal fractions is done in the same way as addition. For example, 44/100 - 1/10 can be solved as 0.44 - 0.1 which is equal to 0.34 or 34/100. Another way to subtract 1/10 from 44/100 is to find the LCM of the denominators and convert them into like fractions. The LCM of 100 and 10 is 100. So, multiply the numerator and denominator of 1/10 by 10.
⇒ 1/10 = (1 × 10)/(10 × 10)
⇒ 1/10 = 10/100
Now, 44/100 - 10/100 = 34/100. Therefore, 44/100 - 1/10 = 34/100.
Multiplying Decimal Fractions
Multiplying decimal fractions is done by multiplying the numerators and denominators separately. To multiply powers of 10, we just add the number of zeros. For example, 7/10 × 3/100 = (7 × 3)/(10 × 100) = 21/1000. To learn more about multiplying fractions, click on the link provided.
Dividing Decimal Fractions
To divide two decimal fractions, follow the steps given below:
- Step 1: Find the reciprocal of the second fraction.
- Step 2: Multiply the first fraction with the reciprocal of the second fraction. That will be the required answer.
This is the same as a normal division of fractions. For example, 25/10 ÷ 5/100 = 25/10 × 100/5. This implies, 5 × 10 = 50. Therefore, 25/10 ÷ 5/100 = 50.
Types of Decimal Fraction
Decimals can be classified into the following types based on their decimal places:
- Terminating decimals
- Non-terminating repeating decimals
- Non-terminating non-repeating decimals
When it comes to decimal fractions, we know that every decimal fraction can be written as a decimal where the number of decimal places is finite and equal to the number of zeros in the power of 10 written in the denominator. So, decimal fractions come in the category of terminating decimals.
Decimal Fraction Conversions
In this section, we will learn how to convert a fraction or a decimal to a decimal fraction. If the denominator of a fraction can be written in the form of prime factorization of either 2 or 5 or both, it means it can be converted to a decimal fraction. For example, in the fraction 3/4, the denominator is 4. 4 can be factorized as 2 × 2. So, this fraction can be converted to a decimal fraction. As 10 is not a multiple of 4, we will look at the next power of 10, which is 100. 100 is the 25th multiple of 4. So, we need to multiply the numerator and denominator of 3/4 by 25 to convert it into a decimal fraction. This implies, 3/4 = (3 × 25)/(4 × 25) = 75/100. Let us take one more example.
Can we convert 5/12 into a decimal fraction? The answer is NO. It is because the denominator 12 cannot be factorized into the product of either 2 or 5 or both.
But don't worry, we can still convert it into a decimal fraction by using another method. Divide 5 by 12. You will get 0.42 approximately. Now, convert this decimal into a decimal fraction. 0.42 is the same as 42/100. Let us learn how to convert a decimal to a decimal fraction by following some simple steps.
- Step 1: Count the number of decimal places in the given decimal number.
- Step 2: Remove the point from the number and divide it by a power of 10 in which the number of zeros will be the same as the number of decimal places counted in the previous step.
Let us convert 0.42 to a fraction. 0.42 has two decimal places. It means we have to divide it by 100 which is the second exponent of 10 (102). Therefore, 0.42 = 42/100.
Look at the decimal fraction chart given below to learn the conversion of some fractions and decimals to decimal fractions.
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Decimal Fraction Examples
Example 1: Susan wants to convert 1/8 to a decimal fraction. Can you help her to do the conversion?
Solution: The given fraction is 1/8. If we multiply the numerator and denominator of 1/8 by 125, we will get 1000 in the denominator. So, 1/8 = (1 × 125)/(8 × 125) = 125/1000. Therefore, 1/8 = 125/1000.
Example 2: Add the following decimal fractions: 35/10 + 12/100.
Solution: To add decimal fractions, let us first find out the LCM of the denominators. The LCM of 10 and 100 is 100. So, multiply the numerator and denominator of 35/10 by 10.
⇒ 35/10 = (35 × 10)/(10 × 10)
⇒ 35/10 = 350/100
Now, 350/100 + 12/100 = (350 + 12)/100 = 362/100. Therefore, 35/10 + 12/100 = 362/100.
Example 3: Select the decimal fractions out of the given options: 3/4, 5/30, 1/11, 121/100, 5/70, 545/1000.
Solution: Decimal fractions are those that have a power of 10 in the denominator. Among the given options, 121/100 and 545/1000 are decimal fractions as the denominators are powers of 10.
Practice Questions on Decimal Fraction
FAQs on Decimal Fraction
What is a Decimal Fraction?
In math, the decimal fraction is defined as those fractions whose denominator is a power of 10. So, there should not be any other number in the denominator instead of 1 followed by zeros. Some of the examples of decimal fractions are 1/10, 3/100, 54/10, etc.
What is a Decimal Fraction and How to Teach it?
Decimal fractions are those that can be written as a decimal using a decimal point. They have a power of 10 in the denominator. Teaching decimal fractions should be done after your learners would be comfortable with the concepts of fractions and decimals. Take any rectangular or circular model divided into 10 or 100 equal parts, and explain decimal fractions as the number of parts taken from the total number of parts (which is a power of 10 in this type). Take decimals as examples and show their conversion into decimal fractions.
What is the Decimal Fraction of Conversion of 18.5?
The given number is 18.5. The decimal fraction of 18.5 is 185/10, as it has 1 decimal place which can be removed to write 10 in the denominator.
How is 1/2 Expressed as a Decimal Fraction?
1/2 as a decimal fraction can be expressed as 5/10.
What Decimal Fraction is 40 ml of a Litre?
In 1 liter, there are 1000 milliliters. The decimal fraction of 40 ml of a liter is 40/1000, which can be further reduced to 4/100.
How to Turn a Decimal into a Decimal Fraction?
To turn a decimal into a decimal fraction, count the number of decimal places and divide the given number by a power of 10 which is the same as the number of decimal places. For example, 0.4 can be written as 4/10, 0.75 can be written as 75/100.