PrintThis chapter will illustrate the exact decimal calculation of fractions like 1/19, 1/29, 1/39 etc… where the unit digit in the denominator has a 9. The next chapter will illustrate general DIVISION rules that apply to all other numbers.
Example: 1/19
Step 1: Calculate the multiplication factor MF = 1 + 1 = 2 (i.e. one more than the previous no. before 9)
Step 2: We will start from right hand side and put 1 (always) as the last digit (i.e. the right most digit) of the answer.
Step 3: Multiply 1 by 2 (which is M.F.) and keep on multiplying by MF2 subsequently (going leftwards)
Step 4: Whenever you get a two digit number keep the unit digit in the answer and carry over ten's digit to the left side as usual
Step 5: We follow this procedure continuously until the digits start repeating
Step 6: Stop when the digit starts repeating. Now put a decimal mark before the first digit a bar over all the digit signifying that it is a non terminating recurring decimal number.
Example:-
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1/19 = .052631578947368421
1 1 1111 1 1 1 (Carried over)
Note that the final answer contains 18 digits. After the decimal we can put a preceding zero before the decimal mark to make the answer more precise
so final answer looks llike:
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1/19 = 0.052631578947368421
Example 2:
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1/29 = 0.0344827586206896551724137931
11 1 2 2 1 2 1 2 2 2 1 1 1 2 1 2 2 (carried over)
Note here MF = 3 (2+1) and the answer contains 28 digits (after the decimal)
1/39 = 0. 025641
here MF = 4
Exercise
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1/49 = 0.020408163265306122448
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979591836734693877551
(MF = 5, No of digits = 42)
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1/59 = 0.0169491525423728813
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559322033898305084 (58 digits)
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1/69 = 0.0144927536231884057971 (22 digits)
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1/79 = 0.0126582278481 (13 digits)
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1/89 = 0.01123595505617975280
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89887640449438202247191 (44 digits)
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1/99 = 0.01
It is important to note the these are exact calculations and we can not get these long answers even with help of a calculator or computer. This illustrates the power and accuracy of Vedic math.
The accuracy of this division method, to a high number of digits, can be used in security codes and in encryption for secure access. Also, it can be used in precision manufacturing and is frequently used in nano technology)
Course:
