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what is 999999999999999999*999999999999999999

 Oct 28, 2020
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Look for patterns!

$$99 \cdot 99=9801$$

$$ 999 \cdot 999 = 998001$$

When looking at the patterns, we see that the formula for the square a number consisting of $n$ $9's$ is:

Number of 9s in the number = Add $n-1$ 9s

Then add an 8

Number of 0s in the number = Add $n-1$ 0s

Then add a 1.

There are 16 digits in the number $999999999999999999.$ So, $$\boxed{999999999999999999^2 = 999999999999999998000000000000000001}$$

 Oct 28, 2020

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