10

$$ e^{\pi \sqrt{163}} \approx 262537412640768743.99999999999925 $$

```
E^(Pi Sqrt[163.0])
N[E^(Pi Sqrt[163.0]), 35]
NumberForm[E^(Pi Sqrt[163.]), 35]
```

returns

```
2.6253741*10^17
2.6253741*10^17
2.625374126407682*10^17
```

That's not the 35 digits I expected. OTOH,

```
N[Pi* E, 35]
```

returns 35 digits,

```
8.5397342226735670654635508695465745
```

but then

```
NumberForm[Pi*E*1., 35]
```

again doesn't:

```
8.53973422267357
```

So I'm confused. Why doesn't one `N[]`

what the other one does? In the documentation:

NumberForm[expr,n]

prints with approximate real numbers inexprgiven ton-digit precision.

I read this three times, slowly, went for a cup of tea, and read it again. But 15 isn't 35, or is it?

1It is, for sufficiently large values of... Okay, the issue, as stated in the response below, is that you cannot get more correct digits after the fact. To obtain 35 digits, use N[] on an exact input, not one that already contains approximate numbers of lower precision. – Daniel Lichtblau – 2012-09-14T14:31:29.940

@Daniel - Thanks for the feedback. Are you referring to my

`163.0`

instead of`163`

? To be honest, I don't know why I wrote it that way :-/ – stevenvh – 2012-09-14T14:35:15.0601Yes, I meant 163.0 was, in effect, polluting the input with machine precision. – Daniel Lichtblau – 2012-09-14T14:36:02.707