How to calculate how many digits in a number from index notation

Question

How can you calculate how many digits are in a number from its index notation?

I need to calculate how many digits are in the number $2^{30} * 5^{25}$

Andrei Kulunchakov · Answer 1 · 2017-02-25T16:23:49.340

2

$2^{30}\times5^{25} = 10^{25}\times2^{5} = 32 \times 10^{25}$

Edit

So, there are two digits for 32 and 25 zeros after it. 27 in total.

edited Feb 25 '17 at 16:23

answered Feb 25 '17 at 16:21

Andrei Kulunchakov

2,452

Is that how many digits are in the number though? – Beastly Gerbil Feb 25 '17 at 16:22
@BeastlyGerbil, see the edit – Andrei Kulunchakov Feb 25 '17 at 16:24
Oh I see now, thanks! I'll accept this when possible – Beastly Gerbil Feb 25 '17 at 16:24

Joffan · Answer 2 · 2017-02-25T16:23:36.693

1

For your particular case, $2^{30} \cdot 5^{25} = 2^5\cdot 10^{25}$, which should be straightforward, given that $10^n$ is the smallest number with $n{+}1$ digits.

edited Feb 25 '17 at 16:23

answered Feb 25 '17 at 16:22

Joffan

39,627

Is that how many digits are in the number though? – Beastly Gerbil Feb 25 '17 at 16:23
Replace $25$ (in $2^5\cdot 10^{25}$) with small numbers like $1,2,3$ to see the pattern. – Joffan Feb 25 '17 at 16:24
I understand now, thanks! – Beastly Gerbil Feb 25 '17 at 16:26

How to calculate how many digits in a number from index notation

2 Answers2