Iam weighed on scales which have a 10% error, that is, the scales show me 10% heavier than my real weight. if i actually weigh 82 kilograms, what will the scales show?

Remember you said the scale shows you 10% heavier.

So that's an increase of 10%

So value = 10% + 100% = 110%

So scale would show  110% of 82

110% of 82

= (110/100)  * 82

= 1.1 * 82

= 90.2

OR

We can simply find 10% of 82 and add it to the original 82.

10% of 82

(10/100) * 82

0.1 * 82 = 8.2

8.2 + 82 = 90.2    Same answer as before.

So scale shows 90.2 kg.