Comparing Decimals
Tenths If a block of one unit is divided into 10 equal parts, then each part is $\frac{\text{1}}{\text{10}}$ (one – tenth) of the unit. It is written as 0.1 in decimal representation. The dot denotes the decimal point. Fractions as Desimal Every fraction whose denominator is 10 can be written in decimal notation.            e.g. $\frac{\text{5}}{\text{10}}$= 0.5 ; $\frac{\text{7}}{\text{10}}$ = 0.7 Hundredths If a block of one unit is divided into 100 equal parts, then each part is $\frac{\text{1}}{\text{100}}$ (one - hundredth)  of the unit.  It is written as 0.01 in decimal notation. Every fraction whose denominator is 100 can be written in decimal notation.           e.g. = 0.05 ;  $\frac{\text{7}}{\text{100}}$ = 0.07 Thousandths If a block of one unit is divided into 1000 equal parts, then each part is $\frac{\text{1}}{\text{1000}}$ (one - thousandth)  of the unit.  It is written as 0.001 in decimal notation. Every fraction whose denominator is 1000 can be written in decimal notation.           e.g. = 0.005 ;  $\frac{\text{7}}{\text{100}}$ = 0.007 To read decimals, we can use the following chart. The first digit to the right after the decimal point represents the tenths parts, the second the hundredths parts, and so on.   Decimal Points   Tenths   Hundredths   Thousandths               .   $\frac{\text{1}}{\text{10}}$   = 0.1         $\frac{\text{1}}{\text{100}}$   = 0.01    $\frac{\text{1}}{\text{1000}}$   = 0.001 Number line All decimal numbers can be represented on the number line. Every decimal number can be represented as a fraction. Comparing desimal Any two decimal numbers can be compared. The comparison starts with the whole part of the numbers. If the whole parts are equal, then the tenth parts can be compared, and so on. Desimals in Real life Decimal numbers are used in many ways in real life. For example, in representing the units of money, length and weight, we use decimal numbers. e.g. Money 100 paise = 1 Rupee 1 paise = 1 / 100 = 0.01 Rupee Length 10 mm = 1 cm 1 mm = 1/ 10 = 0.1 cm 1 cm = 0.01 m 1 m = 0.001 km Weight 1000 g = 1 kg 1 g = 1 / 1000 = 0.001 kg Capacity 1000 ml = 1 litre 1 ml = 1 / 1000 = 0.001 litre

#### Summary

Tenths If a block of one unit is divided into 10 equal parts, then each part is $\frac{\text{1}}{\text{10}}$ (one – tenth) of the unit. It is written as 0.1 in decimal representation. The dot denotes the decimal point. Fractions as Desimal Every fraction whose denominator is 10 can be written in decimal notation.            e.g. $\frac{\text{5}}{\text{10}}$= 0.5 ; $\frac{\text{7}}{\text{10}}$ = 0.7 Hundredths If a block of one unit is divided into 100 equal parts, then each part is $\frac{\text{1}}{\text{100}}$ (one - hundredth)  of the unit.  It is written as 0.01 in decimal notation. Every fraction whose denominator is 100 can be written in decimal notation.           e.g. = 0.05 ;  $\frac{\text{7}}{\text{100}}$ = 0.07 Thousandths If a block of one unit is divided into 1000 equal parts, then each part is $\frac{\text{1}}{\text{1000}}$ (one - thousandth)  of the unit.  It is written as 0.001 in decimal notation. Every fraction whose denominator is 1000 can be written in decimal notation.           e.g. = 0.005 ;  $\frac{\text{7}}{\text{100}}$ = 0.007 To read decimals, we can use the following chart. The first digit to the right after the decimal point represents the tenths parts, the second the hundredths parts, and so on.   Decimal Points   Tenths   Hundredths   Thousandths               .   $\frac{\text{1}}{\text{10}}$   = 0.1         $\frac{\text{1}}{\text{100}}$   = 0.01    $\frac{\text{1}}{\text{1000}}$   = 0.001 Number line All decimal numbers can be represented on the number line. Every decimal number can be represented as a fraction. Comparing desimal Any two decimal numbers can be compared. The comparison starts with the whole part of the numbers. If the whole parts are equal, then the tenth parts can be compared, and so on. Desimals in Real life Decimal numbers are used in many ways in real life. For example, in representing the units of money, length and weight, we use decimal numbers. e.g. Money 100 paise = 1 Rupee 1 paise = 1 / 100 = 0.01 Rupee Length 10 mm = 1 cm 1 mm = 1/ 10 = 0.1 cm 1 cm = 0.01 m 1 m = 0.001 km Weight 1000 g = 1 kg 1 g = 1 / 1000 = 0.001 kg Capacity 1000 ml = 1 litre 1 ml = 1 / 1000 = 0.001 litre

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