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what is the largest number you can add to 6.022x10^23 without changing its display value on a calculator

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The value given is called the Avogadro's number. It is the number of particles in every 1 mole of any substance. I think this is a trial and error process. Input 6.022x10^23 into your calculator. Add to this a number consisting of the maximum digit which is 9. Apparently, when 10×10¹³ is added, the display already changes. Therefore, the largest number would have to be 10×10¹².