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Consider the product 127,500,000,002 ´ 355,700,000,003. Sally says that the digi

ID: 3199579 • Letter: C

Question

Consider the product 127,500,000,002 ´ 355,700,000,003. Sally says that the digit in the one hundred millions place of this product is the ones digit of the number 5 ´ 3 + 2 ´ 7, which is 9. Explain how you can tell that Sally is right without actually multiplying the numbers out completely. What if the multiplication problems had been 127,598,765,432 ´ 355,789,012,343? Would Sally’s reasoning still apply to find the digit in the hundred millions place? Why or why not? Consider the product 127,500,000,002 ´ 355,700,000,003. Sally says that the digit in the one hundred millions place of this product is the ones digit of the number 5 ´ 3 + 2 ´ 7, which is 9. Explain how you can tell that Sally is right without actually multiplying the numbers out completely. What if the multiplication problems had been 127,598,765,432 ´ 355,789,012,343? Would Sally’s reasoning still apply to find the digit in the hundred millions place? Why or why not?

Explanation / Answer

Yes

It is true because

in the given 2 numbers if we can see the numbers to the right of both 5 and 7 are 0's and in unit place we 2 and 3 respectively

as we need to find the digit in one hundred million place

we need to take a look of all digits till that place in the given 2 numbers

but as here all are 0's

we can multiply the digit in one hundred million place with the digit in unit place

hence digit would be = 5 * 3 + 2 * 7 = 15 + 14 = 29

now 9 would be at that place and 2 will carried on to next step.

but in case :2 it is not true because

they are not 0's

hence digit in one hundred millions place = digit in 10's place * digit in 10's millions place + digit in 100's place * digit in millions place .................. ( it continues this way)

hence it is not applicable in 2nd case

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