**Decimal Fractions**

Fractions in which denominators are powers of 10 know a decimal fraction.

Thus,1

101 tenth = .1; 1

1001 hundredth = .01;

99

1001 hundredth = .99; 7

10001 thousandths = .007, etc. **Conversion of a Decimal Into Vulgar Fraction**

Put 1 in the denominator under the deciaml point and annex with it as many zeros as it the number of digits after the decimal point. Now, remove the decimal point and reduce the fraction to its lowest terms.

Thus,.25 = 25

100= 1

4; 2.005 = 2005

1000**Annexing Zeros and Removing Decimal Signs**

Annexing zeros to the extreme right of a decimal fraction does not change its value. Thus, 0.8 = 0.80 = 0.800, etc.

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; 365

584= 5

8**Operations on Decimal Fractions**

1.**Addition and Subtraction of Decimal Fractions**The given numbers are so placed under each that the deciaml 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.**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, 2 x 2 x 2 = 8. Sum of decimal places = (1 + 2 + 3) = 6.

.2 x .02 x .002 = .000008.