Fig 3-1

To Calculate 6 – 2:

1. Find 6 on the lower scale.
2. Place the 2 of the upper scale over 6.
3. the left index (i.e. the 0) of the upper scale indicates the answer as 4 on the lower scale.

When we subtract numbers on the C and D scales we have division.

Fig 3-2

This is because the lengths we are subtracting are the logarithms of the numbers.

Example 1: 6 ÷ 2 = 3 (Fig. 3-2)

1. Set the hair line over 6 on the D scale.
2. Place the 2 of the C scale under the hair line.
3. Below the left index of the C scale read off the answer as 3 on the D scale.

Note: The hair line on the cursor may be used for division in the following ways.

1. To mark the numerator (i.e. number we are dividing into) on the D scale if it does not fall exactly on a graduation, so that the denominator (i.e. number we are dividing by) on the C scale can be set above it.
2. Then to set over the index on the C scale so that the answer can be located on easily on the D scale.

Important Points.

1. When we set up division on the C and D scale it appears seemingly upside down. To calculate 6 ÷ 2 (i.e. ), we find 6 on the (lower) D scale and 2 is placed above it on the (upper) C scale, thus appearing on the Slide Rule as .
2. For division the answer is always indicated on the D scale by the index of the C scale. If the left index of the C scale runs off the end of the D scale, you will notice that the right index will come onto the D scale. Whichever index comes onto the scale, we can use that index to find the answer.

Example 2: 56 ÷ 7 = 8

1. Set the hair line over 56 on the D scale.
2. Place the 7 of the C scale under the hair line.
3. Below the right index of the C scale read off the answer as 8 on the D scale.

Exercise 3(a)

1. =
2. =
3. =
4. 675 ÷ 326 =
5. 196 ÷ 14 =
6. 6.6 ÷ 14.2 =

The best method is to make a quick estimate of the answer. This can be accomplished by several different approaches.

Example 1:

194 ÷ 4.15 = ‘467’

(i.e. approx. 200 ÷ 4 = 50)

therefore the answer is 46.7

Standard form (or scientific notation) may be used when very large or vary small numbers are involved.

Example 2:

56000 ÷ 750 = ‘746’

(i.e. approx. (6 x 10⁴) ÷ (8 x 10²) = .75 x 10²

Good general methods are:

(a) or large numbers divide both numbers by 10, 100, or 1000 etc. (whichever is applicable). That is, cancel corresponding zeros in both numerator and denominator (i.e. top and bottom).

Example 3:

= ‘145’

therefore the answer is 14.5

(b) For small numbers multiply both by 10, 100, 1000 etc., by moving the decimal point a certain number of places to the right as follows.

Example 4:

= ‘688’

(i.e. approx. = ≈ 7

therefore the answer is 6.88

Exercise 3(b)

Locate the decimal point for the following:

1. = ‘878’
2. = ‘306’

 

3. = ‘362’
4. = ‘756’
5. = ‘2175’
6. 9.42 ÷ 216 = ‘436’
7. 0.024 ÷ 0.08 = ‘300’
8. 520 ÷ 0.45 = ‘1155’
9. 0.084 ÷ 0.0025 = ‘336’
10. 43500 ÷ 13.6 = ‘32

Note:

1. When we divide by a number less than 1, the answer is always larger than the number we are dividing into.
2. Unlike multiplication, with division we never run off the end of the D scale for the answer. Either the left or right index of the C scale will always be on the D scale.

When dividing a number by 2 or more numbers, after each division, hold the answer on the D scale with the hair line and repeat the division process as many times as necessary. (For combined multiplication and division see Unit 4).

Miscellaneous Division.