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6              ARMY AIR FORCES

the factors one below the other (see example below). It is usually easier to operate with the smaller number of figures in the bottom row. Multiply the factor in the top row by the right-hand figure of the factor in the bottom row, and write this partial product directly under the second factor. If there is more than one figure in the product the same "carrying over" procedure is followed as in addition. Then multiply the factor in the top row by the second figure from the right in the second factor, and write this second partial product so that its right-hand figure is directly under the figure that was used to find it, There partial products are then added together to yield the required product.
   Example: Multiply 1,653 by 247.
   Solution:
                    1653     FACTORS
                     247
                 [underline]
                   11571
                   6612      PARTIAL
                  3306       PRODUCTS
                 [underline]
                  408291     Answer
                       PRODUCT
                       FIGURE 5.
                              
 b. When there are decimal points, they are ignored until the product has been found. Then the decimal point is inserted in the product according the the following rule: Count off the number of figures to the right of the decimal point in each factor. Then the number of figures to the right of the decimal point in the product is equal to the sum of the number of figures after the decimal point in each factor.
   Example: Multiply 16.53 by 24.7.
   Solution:
                    16.53   2 FIGURES +
                     24.7   1 FIGURE = 
                  [underline] 
                   11571    3 FIGURES
                   6612
                  3306
                  [underline]
                  408.291   Answer
                       PRODUCT
                       Figure 6.

c. When the lower factor contains zeros, the partial products corresponding to these zeros need not all be written down. Only the right-hand zero is written down. However, care must be exercised
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