The modified Pickworth method was developed in the early 1900s and used the idea of characteristics and comparison of the answer's first digit with those of the two values being multiplied or divided.

Characteristic of a Number:

• The characteristic of a number greater than one is the number of digits in front of the decimal point. This characteristic is always positive.
• The characteristic of a number greater than zero but less than one is number of zeros after the decimal point and before the first non-zero digit. This characteristic is always negative.

Example 1:  What is the characteristic of 48799?

• The decimal point would be placed after the last digit, 9.
• There are five digits before the decimal point, so the characteristic is 5.

Example 2:  What is the characteristic of 0.0000567?

• There are four zeros after the decimal point and before the first non-zero digit, so the characteristic is -4.

 

Working with the Characteristics:

• If numbers are multiplied, the characteristics are added.
• If numbers are divided, the characteristics are subtracted; numerator minus the denominator.

 

Rules for Multiplication:

1. When the first significant figure in the product is smaller than either of the factors, the characteristic of the product is equal to the sum of the two characteristics of the factors.
2. When the contrary case is observed, the characteristic of the product is one less than the sum of the two characteristics.

Rules for Division:

1. When the first significant figure of the divisor is greater than that in the dividend, the characteristic of the quotient is found by subtracting the of the divisor from the characteristic of the dividend.
2. When the contrary case is observed, one is to be added to this difference.
3. When the first digits are the same, the following digits must be compared.

 

Example 3: Determine the position of the decimal point and answer for 685 x 0.0000345

• The characteristic of 685 is 3 and the characteristic of 0.000345 is -4.
• Using the slide rule, we read the digits 236.
• The first digit, 2, is less than the first non-zero digits of either factor, so the characteristic of the product is the sum of the characteristics; in this case 3 + (-4) = -1.
• This means that there is one zero in front of the digits of the answer read from the slide rule, hence 0.0236 is the product.

 

Example 4: Determine the position of the decimal point and the answer for 465 x 0.0212

• The characteristic of 465 is 3 and the characteristic of 0.0212 is -1.
• Using the slide rule, we read the digits 986.
• The first digit, 9, is greater than both the non-zero digits of either factor, so the characteristic of the product is the sum of the characteristics minus 1; in this case 3 + (-1) -1 = 1.
• This means that there is only one digit in front of the decimal point, hence 9.86 is the product.

 

Example 5:  Determine the position of the decimal point and the answer for 875 ÷ 0.00345

• The characteristic of 875 is 3 and the characteristic of 0.00345 is -2.
• Using the slide rule, we read the digits 254.
• The first non-zero digit of the divisor, 3 is less than the first non-zero digit of the dividend, 8 so the characteristic of the quotient is the difference of the characteristics plus 1; in this case 3 - (-2) +1 =6.
• This means that there are six digits in front of the decimal point, hence 254000 is the quotient.

 

Example 6:  Determine the position of the decimal point and the answer for 3560 ÷ 0.0855

• The characteristic of 3560 is 4 and the characteristic of 0.0855 is -1.
• Using the slide rule, we read the digits 416.
• The first non-zero digit of the divisor, 8 is greater than the first non-zero digit of the dividend, 3 so the characteristic of the quotient is the difference of the characteristics; in this case 4 - (-1) = 5. 
• This means that there are five digits in front of the decimal point, hence 41600 is the quotient.

 

Example 7:  Determine the position of the decimal point and the answer for 6.65 ÷ 67500

• The characteristic of 6.65 is 1 and the characteristic of 67500 is 5.
• Using the slide rule, we read the digits 985.
• The first non-zero digits of both divisor and dividend are the same, so check the next two.  The digit of the divisor, 7 is greater than the digit of the dividend, 6 so the characteristic of the quotient is the difference of the characteristics; in this case 1 - 5 = -4.
• This means that there are four zeros in front of the digits, hence 0.0000985 is the result.