**I. Decimal Fractions**

**: Fractions in which denominators are powers of 10 are known as**

**decimal fractions.**

**Thus ,1/10=1 tenth=.1;1/100=1 hundredth =.01;**

99/100=99
hundreths=.99;7/1000=7 thousandths=.007,etc

**II.**

**Conversion of a Decimal Into Vulgar Fraction**: Put 1 in the denominator under the decimal point and annex with it as many zeros as is the number of digits after the decimal point. Now, remove the decimal point and reduce the fraction to its lowest terms.

Thus,
0.25=25/100=1/4;2.008=2008/1000=251/125.

**III.**1.

**Annexing zeros to the extreme right of a decimal fraction does not change its value**

Thus, 0.8 = 0.80 = 0.800, etc.

2. If numerator and denominator of a fraction
contain the same number of decimal

places, then we remove the decimal sign.

places, then we remove the decimal sign.

Thus, 1.84/2.99 = 184/299 = 8/13; 0.365/0.584 = 365/584=5

**IV. Operations on Decimal Fractions :**

**1.**

**Addition and Subtraction of Decimal Fractions**: The given numbers are so

placed under each other that the decimal points lie in one column. The numbers

so arranged can now be added or subtracted in the usual way.

2.

point to the right by as many places as is the power of 10.

**Multiplication of a Decimal Fraction By a Power of 10**: Shift the decimalpoint to the right by as many places as is the power of 10.

Thus, 5.9632 x 100 = 596,32; 0.073 x 10000 = 0.0730 x 10000
= 730.

3.

them without the decimal point. Now, in the product, the decimal point is marked

off to obtain as many places of decimal as is the sum of the number of decimal

places in the given numbers.

**Multiplication of Decimal Fractions**: Multiply the given numbers consideringthem without the decimal point. Now, in the product, the decimal point is marked

off to obtain as many places of decimal as is the sum of the number of decimal

places in the given numbers.

Suppose we have to find the
product (.2 x .02 x .002). Now, 2x2x2 = 8. Sum of decimal places = (1 + 2 + 3)
= 6. .2 x .02 x .002 = .000008.

4.

number without considering the decimal point, by the given counting number.

Now, in the quotient, put the decimal point to give as many places of decimal as

there are in the dividend.

**Dividing a Decimal Fraction By a Counting Number :**Divide the givennumber without considering the decimal point, by the given counting number.

Now, in the quotient, put the decimal point to give as many places of decimal as

there are in the dividend.

Suppose we have to find the
quotient (0.0204 + 17). Now, 204 ^ 17 = 12. Dividend contains 4 places of
decimal. So, 0.0204

*+*17 = 0.0012.
5.

**Dividing a Decimal Fraction By a Decimal Fraction :**Multiply both the dividend and the divisor by a suitable power of 10 to make divisor a whole number. Now, proceed as above.
Thus,
0.00066/0.11 = (0.00066*100)/(0.11*100) = (0.066/11) = 0.006V

**V. Comparison of Fractions :**Suppose some fractions are to be arranged in ascending or descending order of magnitude. Then, convert each one of the given fractions in the decimal form, and arrange them accordingly.

Suppose, we have to arrange the
fractions 3/5, 6/7 and 7/9 in descending order.

now, 3/5=0.6,6/7 = 0.857,7/9 =
0.777....

since 0.857>0.777...>0.6, so 6/7>7/9>3/5

**VI. Recurring Decimal :**If in a decimal fraction, a figure or a set of figures is repeated continuously, then such a number is called a

*recurring decimal.*

In a recurring decimal, if a single figure is repeated,
then it is expressed by putting a dot on it. If a set of figures is repeated,
it is expressed by putting a bar on the set

Thus 1/3 = 0.3333….= 0.3;
22 /7 = 3.142857142857.....= 3.142857

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