**DECIMALS**

Are all numbers integers? Well, the obvious answer to that question is a no. All numbers are not integers. Consider the case of 0.333333. What is this number? An integer? Well, it is a decimal. But what are decimals? Decimals are nothing else but the values lying between two integers on the number line.

** Relating decimals to fraction: **When we solve a fraction of the form p/q where q is non-zero, it is not necessarily it would return an integral value. When we are left with a remainder, we ultimately convert it into decimal form. Some examples of Decimals are 4.5, 9.6, 6.78, and 99.98, these all are decimal numbers.

**Tooltip 1: Forming Decimals from Fractions**

How we can write 4/5 in decimal form?

Since the number 4 is smaller than the 5, so the decimal value will be less than one.

Multiple and divide both numbers by 10. We have:

40/ (10 x 5)

Which effectively is (dividing 40 by 5 first) 8/10

Thus, the final result is 0.8 So 4/5 = 0.8 and 0.8 is the decimal form of 4/5.

**Tooltip 2: Adding Decimals **

While adding decimals, you should always write the decimals in a vertical column with the decimal points aligned vertically.

Add all these 0.567 +78+8.9+5.06+56

= 78.000

+ 56.00

+ 5.06

+__0.567__

__ 139.627__

**Tooltip 3: Subtracting Decimal**

In addition we can write the numbers in any order. But while subtracting, we should preferably write the numbers in descending order and the vertical column with decimal points should be aligned to the same decimal points.

Let’s take an example: we have to subtract 0.567 from 5.06. If we write it as:

5.06

__-0.567__

__ 4.507 __

This result is wrong because in case of subtraction we need equal digits in both the quantities, so these blank spaces are filled with 0

So this can be done like as

5.060

__-0.567__

__ 4.493 __

This is the right approach for the question

**Tooltip 4: Multiplying Decimals**

As a first step, multiply the given integers in the normal form keeping the decimals aside. The number of decimal places in the product is then equal to the total of the decimal places in the two decimals. It is as simple as that.

Consider the following example:

5.060

x__0.567__

__2.869020__

First multiply 5060 with 567 and get the result as 2869020 and then move the decimal point to 6 places from the left i.e. between 2 and 8. Effectively, we move it to six decimals places, our sum total of the decimal places in the two numbers.