# Decimal:

Do you ever thought that if there were no any decimal system in early age then if some want to buy only a part of whole then how they did that?

Decimal system helped us to simplify the number system and elevate it. With the help of decimal system you now can take any amount of the whole and pay accordingly by using decimal system.

Dot (∙) represents decimal.

## Tenth:

When a whole object is described in 10 units one part of the whole is said to be tenth of that object.

Similarly 2 part of the whole is said to be 2 tenths and so on.

And the most important thing is when we have to describe 3 part and 2 objects, we can write

3 part of whole = $$\frac{3}{10}$$ also written as 0.3

2 whole = 2

Total = 2 + $$\frac{3}{10}$$ = 2.3 read as two point three.

## Representing Decimals on number line:

We have to represent 0.6 on number line which is 6 part in 10.

## Fractions as decimals:

We can represent any fraction as decimal.

As $$\frac{8}{5}$$ can be written as 10th order.

We multiply its numerator and denominator by 2.
Thus, $$\frac{8}{5}$$ can be written as $$\frac{8×2}{5×2}$$ = $$\frac{16}{10}$$, which can be easily represented in decimal system as 1.6.

## Decimals as fractions:

We can represent any decimal as fraction.

As 3.5 when written in fraction is $$\frac{35}{10}$$ which when divided by equal numbers to numerator and denominator i.e. divide it by 5 we get $$\frac{7}{2}$$.

## Hundredth:

If a whole object contains 100 part and then 1 part of it is called hundredth.

As 5 part of the whole is $$\frac{5}{100}$$ = 0.05

## Comparing Decimals:

When we have to compare two decimal terms as 5.3 and 5.37.

First, we will check the whole part of the two numbers which in these number is same. Then we check its tenth part which is also the same in this case then we will check its hundredth part which in first number is zero and in 2nd number is 7 which is greater than zero.

Thus, second number is greater than the first.

“ We use Decimals in many ways in our lives. For example, in representing units of money, length and weight.”

## Money:

We know that 100 paise = Rs.1

So, 1 paise = Rs. $$\frac{1}{100}$$ = Rs. 0.01

Also, 55 paise = Rs. $$\frac{55}{100}$$ = Rs. 0.55

And Rs1 and 32 paisa = Rs 1.32

## Length:

We know that 1cm = $$\frac{1}{100}$$ m or 0.01 m.

56cm = $$\frac{56}{100}$$ m = 0.56 m

1m and 30 cm =1m + $$\frac{30}{100}$$ = 1.3m

## Weight:

We know that 1000 g = 1 kg

Therefore, 1 g =$$\frac{1}{1000}$$kg = 0.001 kg

## Examples:

1. Write $$\frac{4}{5}$$ as decimal.
Solution:
We must represent it as denominator of 10 as,

$$\frac{4×2}{5×2}$$ = $$\frac{8}{10}$$
= 0.8
2. Write 0.04 as fraction in lowest terms.
Solution:
0.04 = $$\frac{4}{100}$$ = $$\frac{1}{25}$$
3. Write Three hundred six and seven-hundredths as a decimal.
Solution:
We write three hundred six as 306

and seven hundredth as $$\frac{7}{100}$$ = 0.07
thus the total value is 306.07
4. Which is greater in 1.09 and 1.093?
Solution:
09 = 1 + $$\frac{0}{10}$$ + $$\frac{9}{100}$$

1.093 = 1 + $$\frac{0}{10}$$ + $$\frac{9}{100}$$ + $$\frac{3}{1000}$$
As we see the whole part is same in both so we come to the decimal part then we see that the 1.093 has thousandth term greater then 1.09. Thus, 1.093 is greater than 1.09.