The item reciprocal with reference to a number means 1 divided by that number.

Thus, the reciprocal of 1 = 1/1

The reciprocal of 15 = 1/15

The reciprocal of 137 = 1/137

The reciprocal of X = 1/x and so on.

If the values of a variable are small and simple, their reciprocals can be found out directly as cited above. But when the values are of big and complicated forms viz. 43795, 537.5389, etc. and their number is large, it would be difficult to find out their reciprocals in the above manner. In such cases, it is advisable to find out the reciprocals of the numbers with reference to the reciprocal table given at the end of this book. For this, the following steps to be taken up in turn:

**Steps for Finding the Reciprocals from the Table**

1**. **In case of a number of positive character. If, the given number is of positive character i.e., if, it has some significant digits before the decimal point, first put a decimal point, and then put zeroes equal to one less than the number of digits in the unit place of the given number. Then, pick up the digits from the reciprocal table with reference to the first three digits in the given number. If, there are more than 3 digits in the given number, the mean difference for the same should be obtained from the ‘mean difference’ columns of the table with reference to the first two, and the concerned extra columns of the table with reference to the first two, and the concerned extra digit of the number. The mean differences thus obtained should be deducted from the reciprocal originally obtained from the table. In such deduction, the mean differences of each subsequent digit should be placed under the original reciprocal by shifting one place to the right at each subsequent step. When the original number has less than 3 digits, it is to be made of three digits by putting zeroes to its right.

2. In case of a number of negative character. If, he given number is of negative character, i.e., if it has no significant digit before its decimal point, first pick up the digits from the reciprocal table in the manner explained above. Then put a decimal point in the digits thus obtained after one more digit than the number of zeros that appear after the decimal point, and before a significant digit in the given number.

3. In case of a number in which there is only one “1” being either preceded or succeeded by some zeroes, viz : 1, 100, .1, 01, .001,. 0010 etc.:

If the given number comprises only ‘1’ and zeroes (either to its left or to its right, first, obtain the reciprocal in the manner explained above under {are 1 or Pare 2 as the case may be. Then, shift the decimal point of reciprocal by one place only to the right.