Comparing Decimals

Summary

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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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2 . Change into fraction and to its simplest form: 9675.564443

9675.564443 = (9675) + (564443/1000000)

587.6295

0.5 = 5/10 = 1/2

.25

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