Suppose both factors in a multiplication problem are multiples of 10. Why might the number of zeroes in the product be different than the total number of zeroes in the factors?

Multiplying factors whose products are multiples of 10 add to the number of zeros when factors are multiplied as multiples of 10s.

Step-by-step explanation:

Let the first five multiples of ten be

10*1= 10

10*2= 20

10*3=30

10*4=40

10*5= 50

Suppose we chose 20 and 50.

Now multiplying 20 with 50 we get

20*50= 1000

IF we count the total number of zeros in the factors ( 20 and 50) they are 2.

But the number of zeros in the product (1000) are 3.

This is because when we multiply 2 with 5 we get 10 which adds to the existing number of zeros ( i.e 2) and we get a total of 3 zeros.

And multiplying 10 with 50 we get

10*50= 500

IF we count the total number of zeros in the factors ( 10 and 50) they are 2.

But the number of zeros in the product (500) are also 2.

This is because when we multiply 1 with 5 we get 5 which does not add to the existing number of zeros ( i.e 2) and the total number of zeros remain the same.

Similarly multiplying 20 with 30 we get

20*30= 600

IF we count the total number of zeros in the factors ( 20 and 30) they are 2.

But the number of zeros in the product (600) are also 2.

This is because when we multiply 2 with 3 we get 6 which does not have a zero and the total  number of zeros remain the same as in the factors.

So we see that multiplying factors whose products are multiples of 10 add to the number of zeros when factors are multiplied as multiples of 10s.

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step-by-step explanation: