Decimal Fraction

A decimal fraction is a fraction whose denominator is a power of 10, such as 10, 100, 1000, etc. It can be written easily in decimal form using a decimal point.

Types of Decimal Fraction

Decimal fractions can be classified as:

1. Terminating Decimals

Decimal fractions of terminating decimal types have a finite number of digits after the decimal.
For example, 2.345, 7.21458210, 1039.9302. etc.

2. Non-Terminating Repeating Decimals

Decimal fractions of non-terminating decimal types have an infinite number of digits after the decimal.
For example, 2.31313131. . . , 401.103103103 . . . , 21.323232 . . ., etc.

3. Non-Terminating Non-Repeating Decimals

Decimal fractions of non-terminating non-repeating decimals have non-repeating digits after decimals.
For example, e (Euler's Number), π (Pi), 1.01001000100001 . . ., √2, √5, etc.

Operations

We can perform various operations on Decimal Fractions such as addition, subtraction, multiplication or division.

Also Check:

• Addition of Fraction
• Subtracting Fractions
• Multiplying Fractions

Decimal Fractions Percentages

Decimal fractions can be easily converted into percentages by multiplying the decimal fractions into 100 and then applying the % symbol. This can be explained by the example,

Example: Convert 3/10 into a percentage.

Solution:

3/10×100 = 30%

Similarly, we can convert all the decimal fractions into percentages and some of the important decimal fractions as percentages are-

Equivalent Decimal Fractions

Decimal fractions can easily be converted into equivalent fractions by simply simplifying the fraction by dividing the numerator and denominator with the same number. 

Example: Find the equivalent fraction of 4/20.

4/20

Dividing Numerator and Numerator by 4

= 1/5

Similarly, we can convert all the decimal fractions into equivalent fractions and some of the important decimal fractions and their equivalent fraction are given in the table,

Tips and Tricks

1. If the total number of decimal places in the numerator and denominator is the same, the decimal points cancel out. Therefore, we can remove the decimals and solve the expression using integers.

Example: Simplify {\sqrt{\frac{0.009 × 0.036 × 0.016 × 0.08}{ 0.002 × 0.0008 × 0.0002}}}

Count the Decimal Places:

Numerator

• 0.009 → 3 decimals
• 0.036 → 3 decimals
• 0.08 → 2 decimals
• 0.016 → 3 decimals

Total = 11

Denominator

• 0.002 → 3 decimals
• 0.0008 → 4 decimals
• 0.0002 → 4 decimals

Total = 11

Since the total decimal places in both the numerator and denominator are equal, the decimals cancel out.

\sqrt{\frac{9 \times 36 \times 16 \times 8 }{2 \times 8 \times 2}}

\sqrt{9 \times 36 \times 4} = 3 \times 6 \times 2 =36

2. Identify the cube pattern.

Example: Find the value of \bold{(\frac{0.21 \times 0.21 \times0.21 + 0.021 \times 0.021 \times0.021}{ 0.63 \times 0.63\times 0.63 + 0.063 \times 0.063\times 0.063})}

Let a=0.21 and b=0.021

So, 0.63=3 ✕ 0.21=3a and 0.063= 3 ✕ 0.021 =3b

Numerator becomes: a³+b³

and denominator becomes: (3a)³+(3b)³

so, (\frac{(a)^3 + (b)^3 }{(3a)^3 + (3b)^3 })=(\frac{a^3 + b^3 }{27a^3 + 27b^3 })

Taking 27 as common then \frac{1}{27}(\frac{a^3 +b^3 }{a^3 + b^3 }) = \frac{1}{27}

3. Convert both sides into the same base (10) so that powers can be compared.

Example: here , simplifying 10^k = \frac{0.001125}{1.125}\\10^k = 0.001\\10^k = 10^{-3}\\

Now base is same so we can compare powers hence k=-3

4. For repeating decimals.

Example: {\overline{36}} in the form of p/q.

• Let x equal the decimal
• Multiply by powers of 10
• Subtract equations

Let x=0.363636... ---(1)

Multiply by 100 : 100x=36.363636... ---(2)

Subtract equation (1) from (2) : 100x -x = 36.363636... - 0.363636...

99x = 36

x=36/99

x=4/11

Solved Questions and Answers

Question 1: Find the sum of decimal fractions 31/10 and 23/100.

Solution:

= 31/10 + 23/100

= (31/10)×(10/10) + 23/100 [Converting them into like fraction]

= 310/100 + 23/100

= (310 + 23)/100

= 333/100

= 3.33

Question 2: Find the difference of decimal fractions 31/10 and 23/100.

Solution:

= 31/10 - 23/100

= (31/10)×(10/10) - 23/100 [Converting them into like fraction]

= 310/100 - 23/100

= (310 - 23)/100

= 287/100

= 2.87

Question 3: Find the product of decimal fractions 31/10 and 23/100.

Solution:

= 31/10 × 23/100

= (31 × 23)/(10 × 100)

= 713/1000 = 0.713

Question 4: Divide the decimal fractions 31/10 and 23/100.

Solution:

= 31/10 ÷ 23/100

= 31/10 × 100/23

= (31 × 100)/(10 × 23)

= 3100/230

= 310/23

Related Articles:

• Fractions
• Whole Numbers
• Natural Numbers
• Real Numbers