Scale factor/redshift formula wrong at the end?

[Phys12]

In this video:

The professor at the end (at about 7:28), used the formula for scale factor and redshift as a(t) = 1/z, instead of the actual one a(t) = 1/1+z. And when we apply both of them, they give very different results. So, how could the professor use the first formula, which we were never taught about previously and I'm inclined to think is incorrect?

 

[DrSteve]

He's not saying that, but what he does do is confusing. He correctly computes that the scale factor for z = 0.026 is 2.6% smaller, then extrapolates that back to when the scale factor is zero, i.e., the Big Bang, by asking how many times 0.026 goes into 1.

Because he uses the approximation a ~ 1-z it's not obvious that this is rigorous, but the answer he gets is nonetheless correct.

 

[Phys12]

He correctly computes that the scale factor for z = 0.026 is 2.6% smaller, then extrapolates that back to when the scale factor is zero, i.e., the Big Bang, by asking how many times 0.026 goes into 1.

Why would you want to find out how many times 0.026 goes into 1 to find out the scale factor?