**Decimals: **A fraction whose denominator is 10 or some positive integral power of 10 is called a decimal fraction. Examples for decimal fractions are: , .., etc. These decimal fractions can be written in the decimal form as 0.5, 0.37, 0.848, ...., etc. When the decimal fractions are expressed in the decimal form, they are known as decimal numbers (or) decimals. Thus, each of the 0.5, 0.37, 0.848 is a decimal.

A decimal has two parts: whole number part and decimal part. These parts are separated by a dot (.) called decimal point. The part which is left side to decimal point is whole number part and the part which is right side to decimal point is decimal part. For example: In the decimal 421.839, the whole number part = 421 and the decimal part = .839.

**Decimal places: ** The number of digits contained in the decimal part of a decimal gives the number of its decimal places. For example: the decimal 3.89 has 2 decimal places.

**Like decimals:** Decimals having the same number of decimal places are called like decimals. For example: 21.3, 489.2, 987.3, 437.0 all are like decimals because each having one decimal place.

**Unlike decimals:** Decimals having the different number of decimal places are called unlike decimals. For example: 2.97, 51.3 are unlike decimals because in 2.97 we have two decimal places whereas in 51.3 we have only one decimal place.

**Eg: **If you add 6.75 + 4.3 + 2.913 we get

**Sol: **

**Conversion of unlike decimals to like decimals: ** Out of the given unlike decimals find the decimal which has the largest number of decimal places, say 'n'. Convert each of the remaining decimals to the one having 'n' decimal places by annexing the required number of zeros to the extreme right of the decimal part.

**Multiplication of a decimal by 10, 100, 1000, ........., etc:** When decimal is multiplied by some power of 10 then the decimal point is shifted to the right by as many places as is the number of zeros in the multiplier. For example: 73.41 × 10 = 734.1 and 295.867 × 100 = 29586.7.

**Multiplication of a decimal by a whole number:** In this multiplication we have two steps: (i) Without taking the decimal point into consideration, multiply the decimal by the given whole number [i.e., just like the multiplication of two whole numbers] (ii) In the product, put the decimal point in such a way that the resultant decimal has as many places as are there in the multiplicand.

**Multiplication of two or more decimals: ** In this multiplication also we have two steps: (i) Multiply the given decimals without considering their decimal points (ii) In the product, the decimal point is fixed in such a way that the product has as many decimal places as is the sum of the decimal places in the given decimals.

**Dividing a decimal by 10, 100, ...., etc:** To divide a decimal by 10, 100, 1000...etc. shift the decimal point to the left by as many places as is the number of zeros in the divisor. For example: 18.6 ÷ 10 = 1.86 and 219.7 ÷ 100 = 2.197.

**Dividing a decimal by a whole number: **We make ordinary division and mark the decimal point in the quotient as soon as we cross over the decimal point in the dividend.

**Dividing a decimal by a decimal: ** In this division we have two steps: (i) Convert the divisor into a whole number by multiplying the dividend and divisor by a suitable power of 10 (ii) Divide the new dividend by the whole number obtained above.

**Eg: **If 15064 ÷ 28 = 538 then 15.064 ÷ 0.28 = ?

**Sol: **

=53.8

**Simplification using the rule of BODMAS: **In order to simplify a given expression, we must follow the order of simplification as (1) Bracket (2) Of (3) Division (4) Multiplication (5) Addition (6) Subtraction.