## Decimal

Subject: Compulsory Maths

#### Overview

The denominators of the fractions which have the power of 10 then such fractions are called decimal fraction. When a fraction is expressed in decimal and the decimal part is terminated with a certain number of digits, it is called terminating decimal. When the fraction is expressed in decimal and the decimal part is never terminated it is called non-terminating decimal.

#### Decimal

The denominators of the fractions which have the power of 10 then such fractions are called decimal fractions. For example,

$\frac{8}{10}$ = 0.8

$\frac{13}{100}$ = 0.13

Terminating and Non-Terminating recurring decimal

When a fraction is expressed in decimal and the decimal part is terminated with a certain number of digits, it is called terminating decimal.

$\frac{1}{3}$ = 0.3333....

$\frac{1}{6}$ = 0.16666......

$\frac{8}{7}$ = 1.1428571....

Similarly, when the fraction is expressed in decimal and the decimal part is never terminated it is called non-terminating decimal. For example,

$\frac{2}{3}$ = 0.666....

$\frac{7}{9}$ = 0.7777...

$\frac{6}{7}$ = 0.857114285......

Four Fundamental operations on decimals

1. Addition and Subtraction of decimals
While adding and subtracting decimals, we should arrange them in such a way that the digits at the same places should lie in the same column.
+9.08
$\overline{11.58}$
Subtract: 18.79
- 7.843
$\overline{10.947}$
2. Multiplication of decimals
In the case of multiplying a decimal number by 10 or the power of 10. We should simplify shift the decimal point to the right of as many numbers of digits as there are number of zeros in 10, 100, 1000, etc, For example:
Multiply8.367 by 10
8.367× 10 = 83.67
3. Division of decimals
To divide a decimal by another decimal, we should first eliminate the decimal point from the divisor multiplying it by some power of 10. In the same time, the dividend should also be multiplied by the same power of 10. Then we should proceed the division.
Divide 74 by 10
$\frac{74}{10}$ = 7.4
##### Things to remember
• Four Fundamental operations on decimals

1. Addition and Subtraction of decimals
2. Multiplication of decimals
3. Division of decimals
• It includes every relationship which established among the people.
• There can be more than one community in a society. Community smaller than society.
• It is a network of social relationships which cannot see or touched.
• common interests and common objectives are not necessary for society.
##### What is a Decimal?

$\frac{2}{9}$ + $\frac{4}{9}$ =$\frac{2+4}{9}$ = $\frac{6}{9}$ =$\frac{2}{3}$

$\frac{5}{7}$ -$\frac{2}{7}$ =$\frac{5-3}{7}$ =$\frac{3}{7}$

$\frac{1}{3}$ +$\frac{1}{4}$ +$\frac{1}{6}$ = $\frac{1×4+1×3+1×2}{12}$= $\frac{4+3+2}{12}$ = $\frac{9}{12}$ =$\frac{3}{4}$

Solution :

2$\frac{3}{4}$ + 1$\frac{5}{8}$ -3$\frac{1}{3}$

= $\frac{11}{4}$ + $\frac{13}{8}$ -$\frac{10}{3}$

=$\frac{11x6+13x3-10x8}{24}$

=$\frac{66+39-80}{24}$

=$\frac{105-80}{24}$

=$\frac{25}{24}$

=1$\frac{1}{24}$