### 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.

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. Multiplication of a Decimal Fraction By a Power of 10 :

Shift the decimal
point 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.Multiplication of Decimal Fractions :

Multiply the given numbers considering
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.

### 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.