Decimal Fraction – Definition, Examples, Practice Problems

A Decimal Fraction has a power of 10 as the denominator. It is used to represent fractions in their decimal form when the denominator is 10 or a greater power of 10, such as 100, 1000, or 10000. Decimal fractions include 1/10, 1/100, and 1/1000, for instance. Such fractions can be expressed in decimal form as 0.1, 0.01, 0.001, etc. if they are simplified. Mathematical problems involving decimal fractions, such as fraction division and fraction multiplication, are simple to answer.

In this article, we will learn all about decimal fractions as this topic is quite simple but important as well. Students are advised to bookmark this article for future reference so that whenever they want to clear their concept regarding decimal fractions can easily do so.

What is a Decimal Fraction?

A decimal fraction is a way to use a decimal point to indicate a fraction with a denominator of a power of 10 or multiple of a power of 10. This method of writing decimal fractions without a denominator makes it simpler to perform operations on fractions like addition and multiplication.

For Example: 1/10, 1/1000, 1/100, 3/100, 504/1000000000, and so on.

How to Read Decimal Fraction?

If one wants to read a decimal number then one must start with the number that is to the left of the decimal. If there is no number on the left of the decimal point then add a zero and read the decimal part separately.

For Example:

One can read 1234.567 as One thousand two hundred thirty-four point five six seven.

Let’s take another example – One can read 9761.6074 as Nine thousand seven hundred sixty-one point six zero seven four.

Operations on Decimal Fraction

One can perform operations like addition, multiplication, subtraction, and division. Let’s learn one by one.

Addition of Decimal Fraction

If one needs to add 34/100 and 34/1000 then first convert these fractions into decimal fraction form.

34/100 = 0.34 and 34/1000 = 0.034.

Now one can add them easily, 0.34 + 0.034 = 0.374.

Subtraction of Decimal Fraction

If one needs to subtract 34/1000 from 34/100 then first one needs to convert these fractions into decimal fraction form.

34/100 = 0.34 and 34/1000 = 0.034.

Now one can subtract them easily, 0.34 – 0.034 = 0.306

Multiplication of Decimal Fraction

When one wants to multiply a decimal fraction by a power of 10 then one needs to move the decimal point to the right by the number of places that the power of 10 is.

For Example:

1 => 5.4326 × 100 = 543.26

Here the power of 10 is 2 so the decimal is shifted to two places to the right.

2 => 0.1 × 0.01 × 0.001 = 0.000001.

Division of Decimal Fractions

Let’s understand this with an example – 

3444.4/100 = 34.444 and 344.4/100 = 3.444

In both examples, one can observe that when one divides the decimal fraction by 10 or by a multiple of 10 then the decimal part is shifted to the left to an extent of the power of 10.

Types of Decimal Fraction

Now that we have learned about the basic operations, let’s learn about the types of decimal fractions. There are four types of decimal fractions.

1. Terminating Decimal = Those decimals which have a finite number after the decimal point. 

Example – 1.25, 3.15, 1.6, 1.24, etc.

2. Non-Terminating Decimal = Those decimals that have infinite numbers after the decimal point.

Example – 1.41444546856255……., 2.15465…….. etc.

3. Repeating Decimal = Those decimals that have a repeating number that follows a certain pattern are known as Repeating decimals.

Example – 1.414141414141414141……., 1.2525252525252525252……., etc.

4. Non – Repeating Decimal = Those decimals that have a certain number after the decimal but those numbers are not following a certain type of pattern.

Example – 1.41411411141111…….. etc.

Practice Questions on Decimal Fractions

Q1. What decimal of 10 is 2?

A. 0.2

B. 0.02

C. 0.002

D. 0.0002

Answer:

One can solve this as 2/10 = 0.2. Hence option A.

Q2. What is the value of (0.1 × 0.1 × 0.1)?

A. 0.1

B. 0.01

C. 0.001

D. 0.0001

Answer:

One can solve this as 0.1 × 0.1 × 0.1 = 0.001.

Hence option C.

Q3. What is the value of 3412.55 × 1000?

A. 34.1255

B. 3.41255

C. 341.255

D. 3412550

Answer:

One can solve this as 3412.55 × 1000 = 3412550. 

Hence option D.

Q4. What is the value of 3412.55/1000?

A. 34.1255

B. 3.41255

C. 341.255

D. 3412550

Answer:

One can solve this as 3412.55/1000 = 3.41255.

Hence option B.

Q5. What is the value of (10 × 10 × 10 ) / (100 × 100 )?

A. 0.1

B. 0.01

C. 0.001

D. 1

Answer:

One can solve this as (10 × 10 × 10 ) / (100 × 100)

1000/10000 = 0.1

Hence option A.

Q6. What is the value of (0.67 × 0.67 + 0.33 × 0.33 + 2 × 0.67 × 0.33)

A. 1

B. 2

C. 3

D. 4

Answer:

One can solve this as, (0.67 × 0.67 + 0.33 × 0.33 + 2 × 0.67 × 0.33) 

= (0.67)² + (0.33)² + 2 × 0.67 × 0.33 

= (0.67 + 0.33)²

= 1

Hence option A.

Q7. What is the 4114 + 11.44 – 41.14 = ?

A. 4084.3

B. 408.43

C. 40.843

D. 40843

Answer: 

One can solve this as 4114 + 11.44 – 41.14

= 4125.44 – 41.14

= 4084.3

Hence option A.

Q8. What is the value of 0.97 × 0.61 × 0.6 =?

A. 0.35502

B. 3.5502

C. 35.502

D. 355.02

Answer:

One can solve this as 0.97 × 0.61 × 0.6 

= 0.5917 × 0.6

= 0.35502

Hence option A.

Q9. What is the value of 1.2/1.1 = x/22

A. 24

B. 2.4

C. .24

D.  240

Answer:

One can solve this as 1.2/1.1 = x/22

1.2 × 22 = 1.1 × x

26.4 = 1.1 × x

x = 26.4 / 1.1 

x = 24

Hence option A.

Q10. What is the value of 1.44/1.2 = x/2.4

A. 2.88

B. 28.8

C. 288

D. .288

Answer:

One can solve this as 1.44/1.2 = x/2.4

1.44 × 2.4 = 1.2 × x

3.456 = 1.2 × x

x = 3.456/1.2 

x = 2.88

Hence option A.

FAQs on Decimal Fraction

What is a decimal fraction?

The definition of a decimal fraction in mathematics is any fraction with a denominator that is a power of 10. Therefore, the denominator must only include 1 and zeros like the numerator. Decimal fractions can be expressed as 1/10, 5/100, 67/10, etc.

How do you write a decimal fraction?

Fractions can be used to represent decimals. Place the decimal number above its place value to convert it to a fraction.

What is a decimal fraction in the simplest form?

The basic in-divisible fraction that results from dividing the numerator by the denominator is the most fundamental form of a decimal fraction. For instance, 6/5 is the simplest representation of the decimal fraction 12/10.

Where are decimal fractions used?

The weight of persons and goods is expressed using decimal fractions. Additionally, it can be used to calculate product price discounts and measure the ingredients in recipes.

What is a decimal fraction example?

The decimal version of fractions with a denominator of 10 or greater powers of 10, such as 100, 1000, or 10000, are represented as decimal fractions. They include 1/10, 1/100, and 1/1000, for instance. Such fractions can be expressed in decimal form as 0.1, 0.01, 0.001, etc. if they are simplified.