Decimals : Decimals are an extension of our number system. Decimals are fractions whose denominators  are 10, 100, 1000 etc. A decimal has two parts, namely, the whole number part and decimal part.

 

Decimal Places : The number of digits contained in the decimal part of a decimal number is known as the number of decimal places.

For :

3.75 has two decimal places and 85.325 has three decimal places.

 

Like and unlike decimals : Decimals having the same number of decimals places are called like decimals, otherwise they are known as unlike decimals.

For example :

5.25, 15.04, 273.89 are like decimals and 9.5, 18.235, 20.0254 etc. are unlike decimals.

 

We have 0.1 = 0.10 = 0.100 etc, 0.5 = 0.50 etc. and so on. That is by annexing zeros on the right side of the extreme right digit of the decimal part of a number does not alter the value of the number. 

Unlike decimals may be converted into like decimals by annexing the requisite number of zeros on the right side of the extreme right digit in the decimal part.

 

If an object is divided into 10 equal parts then its each part is one tenth of the whole. It is written as 1/10. 1/10 is also written as 0.1 and is read as 'one tenth' or 'decimal one or point one'. thus 1 ones = 10 tenth Ex. 0.5 is read as 5 tenth.

 

        We have learnt the representation of whole numbers and fractions on a number line. Now we shall explain the method of representing decimal numbers on number line

Let us represent 1.3 on a number line 

 

1.3 is more than 1 and less than 2 

1.3 is 1 + 0.3, i.e 1 + 3 tenths

Draw a number line and mark whole numbers 0,1 ,2,3, ....... on it.

Divide the portion between 1 and 2 into 10 equal parts and take 3 parts for 3 tenths or 0.3 Mark it as P. In the above figure P presents the number 1.3.

Ex. Mark the following decimals in place value table :

(a) 0.3 (b) 19.4 (c) 205.9

Sol. Place Value Table

 

 

Ex. Write the following in decimal fractions :

(a) 0.8 (b) 1.3

Sol. (a) 0.8 = 8 tenths = 8/10

 

(b) 1.3 = 1 + 3 tenths = 1 +  3/10 

Ex. Write the following as fractions. Reduce them to lowest terms :

(a) 1.0 (b) 3.8

(c) 21.2

Sol. (a) 1.0 = 1

(b) 3.8 = 3 ⁸/10

(c) 21.2 = 21²/10 = 21

 

If an object is divided into 100 equal parts then its each part is one hundredth of the whole. It is written as 1/100.1/100  is also written as 0.01 and is read as 'one hundredth' or 'decimal zero one' or zero point zero one'.

 

If an object is divided into 1000 equal parts then its each part is o
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