# Thread: First digit after comma

1. ## First digit after comma

Find first digit after comma of expression $\displaystyle (\sqrt2+\sqrt3)^{2008}$

2. Originally Posted by terafull
Find first digit after comma of expression $\displaystyle (\sqrt2+\sqrt3)^{2008}$
What comma?

3. Originally Posted by Plato
What comma?
I think he means "decimal point" for us US people.

-Dan

4. Yes, I meant decimal point.

5. $\displaystyle 2008log(\sqrt{2}+\sqrt{3})=999.5728$

Now, take $\displaystyle 10^{.5728}=3.7394$

Those are the first few digits of this big number with about 1000 digits.

6. I dont understand why like this. And 3 is the first digit after decimal point or 7?

$\displaystyle (\sqrt2+\sqrt3)^{2008}=10^{2008log(\sqrt2+\sqrt3)} =10^{999.5728}=10^{999}*10^{0.5728}$
And what now?

7. Originally Posted by galactus
$\displaystyle 2008log(\sqrt{2}+\sqrt{3})=999.5728$

Now, take $\displaystyle 10^{.5728}=3.7394$

Those are the first few digits of this big number with about 1000 digits.
But I must know first digit after decimal point.

8. I pretty much gave you the answer. Look at it. There are 1000 digits in the number. Therefore, counting off blocks of 3 from the far right of this huge number gives us 3,739,..................

So, the next number after the comma is 7.

You could even run it through a calculator. My TI-92 gives me

3.7392622716E999

So, there are 999 digits after the 3 and the first one is 7.

BTW, do you use decimal points instead of commas in Europe or wherever?.

In the US, it's commas to separate the 1000's.

For instance, 1,000,000,000

Would you write 1.000.000.000?

If so, that's wacky and wrong. Do it the right way.

9. Originally Posted by galactus
I pretty much gave you the answer. Look at it. There are 1000 digits in the number. Therefore, counting off blocks of 3 from the far right of this huge number gives us 3,739,..................

So, the next number after the comma is 7.

You could even run it through a calculator. My TI-92 gives me

3.7392622716E999

So, there are 999 digits after the 3 and the first one is 7.

BTW, do you use decimal points instead of commas in Europe or wherever?.

In the US, it's commas to separate the 1000's.

For instance, 1,000,000,000

Would you write 1.000.000.000?

If so, that's wacky and wrong. Do it the right way.
OK, thanks. I mean decimal point, not comma.. So, I must find first digit after decimal point of this expression.
In Europe are 1/4=0,25 and 10^5=10.000 or =10 000.