Question

what digit out of 1, 3,5, and 9 would complete the second factor so that the product will have 2 decimal places for 7.2 x 4.6____

Answer 1

When we have multiple possibilities for a number, we can replace it with a letter (or variable) -- here, we can put the second decimal place for 4.6_ as y. Therefore, when we multiply the two numbers, 7.2*4.6y=

        7.2

    x  4.6y

__________

        7.2*y

       4.320

     28.800  

Therefore, if we add 28.8 and 4.32 up, we are at 33.12. Aligning the zeros, it is clear that if the last digit of 7.2*y is not 0, this equation will end up having more than 2 decimal places. Therefore, using a little guess and check, we have 7.2*1=7.2, 7.2*3=21.6, 7.2*5=36.0, and 7.2*9=648. Therefore, 5 is our answer.

Feel free to ask further questions, and Happy Holidays!