PLACING THE DECIMAL POINT
Various methods have been advanced regarding the placement of the
decimal point in numbers derived from slide rule computations.
Probably the most universal and most easily
remembered method is that of approximation.
The method of approximation means simply the
rounding off of numbers and the mechanical shifting
of decimal points in the numbers of the problem
so that the approximate size of the solution
and the exact position of the decimal point
will be seen from inspection. The slide rule
may then be used to derive the correct sequence of significant digits. The
method may best be demonstrated by a few
examples. Remember, shifting the decimal point in a number one
place to the left is the same as dividing by 10.
Shifting it one place to the right is the same
as multiplying by 10. Every shift must be
compensated for in order for the solution to be
correct.
EXAMPLE: 0.573 x 1.45
SOLUTION: No shifting of decimals is necessary here. We see that
approximately 0.6 is to be multiplied by
approximately 1 1/2. Immediately, we see that the solution is in the
neighborhood of 0.9. By slide rule we find that the significant
digit sequence of the product is 832. From
our approximation we know that the decimal point is to the immediate left of the
first significant digit, 8. Thus,
0.573 x 1.45 = 0.832
EXAMPLE: 239 x 52.3
SOLUTION: For ease in multiplying, we shift the
decimal point in 52.3 one place to the left, making
it 5.23. To compensate, the decimal point is
shifted to the right one place in the other
factor. The new position of the decimal point
is indicated by the presence of the caret symbol.
239.0_{^} x 5_{^}2.3
Our problem is approximately the same as
2,400 x 5 = 12,000
By slide rule the digit sequence is 125. Thus,
239 x 52.3 = 12,500
EXAMPLE: 0.000134 x 0.092
SOLUTION:
Shifting decimal points, we have
0_{^}00.000134 x 0.09_{^}2
Approximation: 9 x 0.0000013 = 0.0000117. By
slide rule the digit sequence is 123. From approximation
the decimal point is located as follows:
0.0000123
Thus,
0.000134 x 0.092 = 0.0000123
Example:
SOLUTION: The decimal points are shifted so that
the divisor becomes a number between 1 and
10. The method employed is cancellation. Shifting
decimal points, we have
Approximation: 5/4 = 1.2
Digit sequence by slide rule:
1255
Placing the decimal point from the approximation:
1.255
Thus,
Example
SOLUTION:
Shifting decimal points
Approximation:
Digit sequence by slide rule: 690
Placing the decimal point from the approximation:
0.0690
Thus,
Practice problems. Solve the following problems
with the slide rule and use the method of
approximation to determine the position of the
decimal point:
Answers:
1. 0.000745
2. 42.4
3. 0.0438
4. 0.212
