## Arithmatical - Decimal Fraction

Important Facts and Formulae
1. 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 = 0.1;
2. 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;
3. 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, .365 / .584 = 365 / 584 = 5 / 8.

4. Operations on Decimal Fractions :I). 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.II). 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.III). Multiplication of Decimal Fractions: Multiply the given numbers considering them without 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 0.02 x .002).Now, 2 x 2 x 2 = 8. Sum of decimal places = (1 + 2 + 3) = 6.Therefore, .2 x .02 x .002 = .000008
5. Dividing a Decimal Fraction By a Counting Number :Divide the given 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.
6. 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 x 100 /0.11 x 100 = 0.066/11 = .006.