What are Decimal Fractions?
Fractions in which denominators are powers of 10 are known as decimal fractions.
Examples : 1/10 = 1 tenth = 0.1; 9/1000 = 9 thousandths = 0.009
Converting a decimal into vulgar fraction
1 is put in the denominator just below the decimal point. Now as many zeros are annexed to the denominator as is the number of digits after the decimal point. Then the decimal point is removed and the fraction is reduced to its lowest terms.
Example : 0.25 = 25/100 = 1/4
Some Important Results
Annexing zeros to the extreme right of a decimal fraction does not change its value.
If numerator and denominator of a fraction has same number of decimal places, then the decimal point is removed.
Operations on Decimal Fractions
a) Addition and Subtraction
The numbers are placed under each other so that the decimal points lie in one column. Now the numbers are added or subtracted in the usual way.
b) Multiplication
The given numbers are multiplied without taking into account the decimal point. In the product as many decimal places are marked off as is the sum of the number of decimal places in the given numbers
Example : 2.5 x 0.5
First we multiply the numbers without decimal point. 25 x 5 = 125.
Now, sum of decimal places = (1 + 1) = 2. Then product of 2.5 and 0.5 is 1.25
c) Division by a natural number
The given number is divided by the natural number without considering the decimal point. Now in the quotient the decimal point is put to give as many decimal places as there are in the dividend.
d) Division by a decimal fraction
Both the dividend and the divisor is multiplied by a power of 10 so that the divisor becomes a whole number. Now the dividend is divided by the divisor.
Recurring Decimal
If in a decimal fraction, a figure or a set of figures is repeated continuously then it is called non-terminating or recurring decimal.
In a recurring decimal, if one figure is only repeated then it is expressed by putting a dot or bar over it. If a set of numbers is repeated then it is expressed by putting a dot on the first and last digit of the set or by putting a bar over it.
Pure Recurring Decimal
In a decimal fraction, if all the figures after the decimal point is repeated then it is called a pure recurring decimal.
Mixed Recurring Decimal
A decimal fraction in which some figures do not repeat and some of them are repeated, is called a mixed recurring decimal.
Fractions in which denominators are powers of 10 are known as decimal fractions.
Examples : 1/10 = 1 tenth = 0.1; 9/1000 = 9 thousandths = 0.009
Converting a decimal into vulgar fraction
1 is put in the denominator just below the decimal point. Now as many zeros are annexed to the denominator as is the number of digits after the decimal point. Then the decimal point is removed and the fraction is reduced to its lowest terms.
Example : 0.25 = 25/100 = 1/4
Some Important Results
Annexing zeros to the extreme right of a decimal fraction does not change its value.
If numerator and denominator of a fraction has same number of decimal places, then the decimal point is removed.
Operations on Decimal Fractions
a) Addition and Subtraction
The numbers are placed under each other so that the decimal points lie in one column. Now the numbers are added or subtracted in the usual way.
b) Multiplication
The given numbers are multiplied without taking into account the decimal point. In the product as many decimal places are marked off as is the sum of the number of decimal places in the given numbers
Example : 2.5 x 0.5
First we multiply the numbers without decimal point. 25 x 5 = 125.
Now, sum of decimal places = (1 + 1) = 2. Then product of 2.5 and 0.5 is 1.25
c) Division by a natural number
The given number is divided by the natural number without considering the decimal point. Now in the quotient the decimal point is put to give as many decimal places as there are in the dividend.
d) Division by a decimal fraction
Both the dividend and the divisor is multiplied by a power of 10 so that the divisor becomes a whole number. Now the dividend is divided by the divisor.
Recurring Decimal
If in a decimal fraction, a figure or a set of figures is repeated continuously then it is called non-terminating or recurring decimal.
In a recurring decimal, if one figure is only repeated then it is expressed by putting a dot or bar over it. If a set of numbers is repeated then it is expressed by putting a dot on the first and last digit of the set or by putting a bar over it.
Pure Recurring Decimal
In a decimal fraction, if all the figures after the decimal point is repeated then it is called a pure recurring decimal.
Mixed Recurring Decimal
A decimal fraction in which some figures do not repeat and some of them are repeated, is called a mixed recurring decimal.
