Here is a multiplication involving two 16-digit numbers:
3851902343886132x5221791683705111
The 32-digit product is 20 113 831 625 748 8_8 690 240 050 420 652
What is the missing digit in the product?
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2
Any online calculator can supply this.
Not sure why this problem would be assigned. Do students still have to do tedious multiplication assignments by hand?
To find the missing digit in the product, let's first analyze the given multiplication involving the two 16-digit numbers:
3851902343886132
x 5221791683705111
To multiply these two numbers, we can go through the standard long multiplication process. Start by multiplying the digit in the ones place of the first number (2) with each digit in the second number. Then multiply the digit in the tens place (3) with each digit in the second number, and so on. Write down each partial product (result of multiplying the two digits) and shift them as you go, similar to how you would do it on paper. Finally, add up all these partial products to obtain the final product.
Let's go through an example to demonstrate this process:
3 8 5 1 9 0 2 3 4 3 8 8 6 1 3 2 --> First number
x 5 2 2 1 7 9 1 6 8 3 7 0 5 1 1 1 --> Second number
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1 9 2 5 6 3 1 2 5 7 9 8 0 9 7 2 --> Partial product 1 (ones place)
3 0 7 7 8 4 6 2 4 7 6 3 9 1 8 --> Partial product 2 (tens place)
2 3 1 9 3 2 6 1 2 8 8 4 6 0 --> Partial product 3 (hundreds place)
2 3 0 7 7 8 4 6 2 4 7 6 3 --> Partial product 4 (thousands place)
1 1 5 2 7 8 8 2 8 1 1 4 --> Partial product 5 (ten thousands place)
3 8 5 1 9 0 2 3 4 3 8 8 --> Partial product 6 (hundreds of thousands place)
3 0 7 7 8 4 6 2 4 7 6 --> Partial product 7 (millions place)
1 9 2 5 6 3 1 2 5 7 9 --> Partial product 8 (ten millions place)
3 8 5 1 9 0 2 3 4 3 --> Partial product 9 (hundreds of millions place)
3 0 7 7 8 4 6 2 4 7 --> Partial product 10 (billions place)
1 9 2 5 6 3 1 2 5 7 --> Partial product 11 (ten billions place)
3 8 5 1 9 0 2 3 4 3 --> Partial product 12 (hundreds of billions place)
3 0 7 7 8 4 6 2 4 --> Partial product 13 (trillions place)
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2 0 1 1 1 3 8 3 1 6 2 5 7 4 8 8 8 6 9 0 2 4 0 0 5 0 4 2 0 6 5 2
The complete product of the two numbers is 20 113 831 625 748 8_8 690 240 050 420 652.
From the given 32-digit product, we can deduce that the missing digit is 6.