**Best explanation to understand and solve the decimal fraction**

This section is related to the aptitude topic DECIMAL FRACTION. This topic is very important and we use this math in our day to day life.

Decimal fraction is also one of the important topics in aptitude. You will have questions based on decimal fraction aptitude in most of the bank exams and entrance exams.

So to make it easy for we are providing you this article with all that you need to know.

This article will help you to clearly understand the concept of decimal fraction and its important formulas.

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**What is decimal fraction?**

Any integer number that is separated by a decimal point is known as a decimal fraction.

For example, the numbers 0.2, 0.47, 0.01011, etc are some decimal fractions.

If we convert the number into a vulgar fraction, the number’s denominator will contain 10 or a multiple of 10. For example, the number 0.1 = 1/10 and 0.55 = 55/100

**What is called decimal places?**

The number of figures which follow the decimal point is called the number of decimal places. Thus, 3.625 can be written as 3625/1000 that means we have three decimal places, and 5.39 have two decimal places.

**How to convert decimal into vulgar fraction?**

Write down the given number without the decimal point for the numerator, and denominator write 1 followed by as many zeros as many are the figures after the decimal point. For example: 3.423 = 3423/1000.

1. Adding zeros to the extreme right of a decimal fraction does not change its value.

For example, 0.4 = 0.40=0.400=0.4000000

2. If numerator and denominator have the same number of decimal places, we can remove the decimal sign.

For example, 0.72/0.18 is equal to 72/18.

3. If numerator and denominator have different number of decimal places, we have to equate both numbers of figures in decimal part by putting zeros, and then remove the decimals.

For example, 10/ 2.5 = 100/25 = 4

**How to calculate addition and subtraction in decimal?**

Write down the numbers, placing the decimal points in one column. The numbers can now be added or subtracted in the usual way.

For example: 13.725 + 6.275 = 20.000 = 20

Subtraction: 13.72 – 3.225 is equals to 13.720 – 3.225 = 10.495

**How to multiply decimals?**

To multiply by 10, 100, 1000, etc., Move the decimal points by as many places to right as many are the zeros in the multiplier.

For example, 12.5*10 =125

To multiply by a whole number: Multiply the number as in the case of integers and place the decimal point in the product as many decimal places as in the multiplicand, prefixing zeros, if necessary.

For example, 12.5*7

Multiplicand = 12.5

Multiplier = 7

Now, Step 1: multiply by taking both of them as the integer value

125*7 = 875

Step 2: place the decimal in the product as many decimal places as in the multiplicand.

ATQ, the multiplicand has 1 decimal place.

So, the product will be 87.5 (decimal point after 1 decimal place).

To multiply a decimal by a decimal: multiply as in integer, and place the decimal in product value as many decimal places as there are in the case of the multiplier and the multiplicand together, prefixing zeros, if necessary.

For example, 12.5*7.325

Multiplicand = 12.5

Multiplier = 7.325

Step 1: multiply by taking both of them as the integer value

125*7325 = 915625

Step 2: place the decimal point in the product as many decimal places as there are in the case of the multiplier and the multiplicand together.

ATQ, multiplicand has 1 decimal place, and multiplier has three decimal places.

That means the Product will contain the decimal point after 1+3 = 4 decimal places.

So, the product of 12.5 * 7.325 = 91.5625

**How to divide decimals?**

When the divisor is 10, 100, 1000, etc., To divide a decimal by 10, 100, 1000, etc., move the decimal point 1, 2, 3, etc., places to the left respectively.

For example, 12.23/10 = 1.223 and 153.56/1000 = 0.15356

When the divisor is a decimal fraction: Move the decimal point as many places to the right in the divisor to make the divisor as a whole number, annexing zeros to the dividend as many places as you moved the point to the right in the divisor.

For example, 125/5.5

annexing zeros in the dividend to make the divisor as a whole number.

1250/55 = 22.7272…..

**What is recurring decimal?**

A decimal in which a figure or set of figures is repeated continually is called a recurring or periodic or circulating decimal. The repeated figures are a set of figures which is called the period of a decimal.

**Pure recurring decimal**: A decimal number, in which all the digits after the decimal points are repeated, is called a pure recurring decimal.

For example, 2.3̅2̅1 is a pure recurring decimal because all the numbers after the decimal point are repeated.

**Mixed recurring decimal**: A decimal number in which some digits do not recur after the decimal point, is called a mixed recurring decimal. For example, 0.5429 is a mixed recurring decimal because out of 542̅9 only 2 and 9 are recurring.

**How to convert a recurring decimal fraction into vulgur fraction?**

**Pure recurring decimal to vulgar fraction**: A pure recurring decimal can be written as the vulgar fraction by putting as many nines as there are recurring digits after the decimal point, in the denominator of the vulgar fraction.

For example, 0.3̅2̅1= 321/999 and 3.2̅5 = 3+ 25 / 99

**Mixed recurring decimal to vulgar fraction**: A mixed recurring decimal can be written as a vulgar fraction in which the numerator will contain the difference between the number formed by all the digits (after the decimal point) and the numbers that do not recur; and the denominator will contain as many nines as there recurring digits, followed by as many zeros as there are non-recurring digits.

For example, the number 0.32145 can be expressed as [32145- 321]/ 99000

**How to calculate the addition and subtraction of recurring decimal?**

**Pure recurring decimal**: First we have to convert the recurring decimal into an integer and then perform the addition or subtraction.

For example, the number 13.2̅4+ 15.2̅7 will add in two parts.

Add the integer value that is on the left-hand side of the decimal point Or, 13+15 = 28

Now add the recurring value that is on the right-hand side of the decimal point Or, 24+27 = 51

Hence, the addition of 13.2̅4+ 15.2̅7 = 28.5̅1

**What is mixed recurring decimal?**

Addition and subtraction of mixed recurring decimals can be done in the following steps:

Separate the expansion of recurring decimals into three parts. In the left-side part, there is an integer value with non-recurring decimal digits. In case of only one number contains the non-recurring value then the other one who has only recurring value will place his recurring value to make the same decimal place in both numbers.

In the middle part, we have to count that how many recurring values are in the first number and the second number, and then take the LCM of both. Repeat the recurring number LCM’s number of times in the middle part.

In the last part, it doesn’t matter that how many recurring digits are there in the numbers, we have to put two recurring digits always in the third-part.

**What is multiplication of recurring decimal?**

While multiplying a recurring decimal by a multiple of 10, the set of repeating digits is not altered. For example, let the multiplicand = 3.5̅7, and multiplier = 10

Now, 3.5̅7 can be written as 3.575757…. * 10 = 35.7575757…..

We know that the repeating value will not be altering so the recurring number will be the same. i.e., 35.75̅7̅5̅7̅5̅7

While multiplying a recurring decimal by a number which is not a multiple of 10, first all of the recurring decimal is changed into a vulgar fraction, and then the calculation is done.

For example, let the multiplicand = 7.6̅3̅, and multiplier = 11

Now, 7.6̅3 can be written as 7+ 63 / 99 x 11

or, (7 + 7 / 11) x 11 = 11 x 7 +7 = 84

so, the result will be 84

**What is approximation and contraction?**

Increase the figure after the decimal point to the nearest 10 if the succeeding figure is 5 or greater than 5.

For example, the approximate value of 10.68 is 10.7

**How to calculate lcm and hcf of decimal fraction?**

The HCF and the LCM of a decimal number can be found in two steps:

First, you have two make the number of digits (value after decimal) equal in the decimal numbers by adding zeros in the suffix if necessary.

Now assume that both the numbers are an integer and then get the HCF and LCM of that number. Place the decimal point in the result as many decimal places as in the in the initial number.

For example, 0.36 and 1.08

Now, express each of the numbers without decimals as the product of primes and we get:

36 = 2 × 2 × 3 × 3 = 22 × 32

108 = 2 × 2 × 3 × 3 × 3 = 22 × 33

Now, H.C.F. of 36 and 108 = 22 × 32 = 36

Therefore, the H.C.F. of 0.36 and 1.08 = 0.36 (taking 2 decimal places)

L.C.M. of 36 and 108 = 22 × 33 = 108

Therefore, L.C.M. of 0.36 and 1.08 = 1.08 (taking 2 decimal places)

### What is comparison of fraction?

Convert each one of the given fractions in the decimal form. Now, arrange them in the required order.

For example, 3/10, 10/7, 5/9 Convert them in decimal form:

3/10= 0.3

10/7 = 1.428

5/9 = 0.555…

Now compare each and arrange in ascending or descending order.

Ascending order: 0.3<0.555<1.428

Or 3/10 < 5/9 < 10/7

So yes, these are the important concepts that you need to know before attending the aptitude on decimal fraction.

It is one of the most important and also a big concept. You need to read this article completely to avoid confusions.

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