A single gram of a certain metallic substance has 0.52 grams of copper and 0.26 grams of zinc. The remaining portion of the substances is nickel. Ben estimated that 0.2 gram of nickel is 1 gram of the substance. He used this to estimate the amount of nickel in 35 grams of the substance. Find the result of Ben’s estimation strategy. Then, find the exact amount of nickel in 35 grams of the substance.

Ben's estimation strategy gives him an answer of 7 g of nickel in 35 g of the substance. 
The exact answer is there is 7.7 g of nickel in 35 g of the substance.

Using a proportion for Ben's estimate, we set the first ratio as 0.2/1, since he states there are around 0.2 g of nickel in 1 g of the substance.  The other ratio would be x/35, with x representing the amount of nickel and 35 being the amount of the substance:

0.2/1 = x/35

Cross multiply:
0.2*35 = 1*x
7 = x

Ben's estimate is 7.

There are 0.52 g of copper and 0.26 g of zinc in 1 g of the substance.  This makes up 0.52+0.26 = 0.78 g out of 1 g total.  To find the remaining amount (nickel), subtract from 1:
1 - 0.78 = 0.22

There are 0.22 g of nickel in 1 g of the substance.

This means there are 0.22*35 = 7.7 g of nickel in 35 g of the substance.