# In between the years, a PISA question (nothing essential): The last digit of 7^190

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Last digit of 7^190, I thought a simple question if you have Matlab. But

fprintf('%f\n',7.0^190.0)

reports 4 as last digit, but it must be an odd number. 7^190 is fare away from realmax. Why that? It's not a big issue, only for my understanding.

##### 1 Comment

Stephen23
on 28 Dec 2023

Edited: Stephen23
on 28 Dec 2023

"7^190 is fare away from realmax"

REALMAX is irrelevant.

The value is well above FLINTMAX (so, as the documentation states, your value is outside the range of consecutive integer values), so there is no expectation that your value will be represented accurately down to the ones:

### Accepted Answer

Paul
on 28 Dec 2023

##### 16 Comments

Rik
on 29 Dec 2023

Though Steven is technically correct that realmax is the largest integer that can be represented by a double, stating this is not helpful, as people will misinterpret it. Realmax does represent an integer, but since multiple numbers will map to realmax, its uses are limited. If you want to guarantee the correct last digit, flintmax is the limit.

There have been efforts to implement the quad datatype in Matlab, though to my knowledge that didn't reach a practical state. That would push flintmax to 2^113-1 (if I understand it correctly). Still not enough for this question, but a lot better.

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