Problems from Multiplication and division of decimal numbers

Define two decimal numbers a and b of 3 digits of integer part and 3 digits of fractional part. Calculate its product and the a/b division. Note: Use the following matrix to calculate the product:

            a5 a4 a3 a2 a1 a0
X           b5 b4 b3 b2 b1 b0
                       
                       
                       
                       
                       
                       
= x x x x x x x x x x x

where a0a5, b0b5 are the digits of a and b, respectively, and x the digits of the result.

See development and solution

Development:

a=783,623

b=126,961

ab: The product is done without fractional digits and the comma is placed so that it has 3+3=6 fractional digits.

            7 8 3, 6 2 3
X           1 2 6, 9 6 1
            7 8 3 6 2 3
        4 7 0 1 7 3 8  
      7 0 5 2 6 0 7    
    4 7 0 1 7 3 8      
  1 5 6 7 2 4 6        
  7 8 3 6 2 3          
= 9 9 4 8 9, 5 5 9 7 0 3

ab: since the number of decimal is the same in a and b, the commas can be ignored, and now compute the division of the integers (a1000)(b1000) ab=6,17

Solution:

ab=99489,56

ab=6,17

Hide solution and development
View theory