In India, the day ‘December 22′ has been declared as the National Mathematics Day. The declaration was made by Prime Minister of India, during the inaugural ceremony of the celebrations to mark the 125th birth anniversary of SrinivasaRamanujan held at the Madras University Centenary Auditorium on 26 February 2012. Dr Manmohan Singh also announced that the year 2012 CE would be celebrated as the National Mathematics Year. The Indian mathematical genius SrinivasaRamanujan was born on 22 December 1887 (Erode, Tamil Nadu) and died on 26 April 1920. It was in recognition of his contribution to mathematics the Government of India decided to celebrate Ramanujan’s birthday as the National Mathematics Day every year and to celebrate 2012 as the National Mathematical Year.
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. AXIOM
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.
4.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. 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