Is there a name for this theorem?

Question

Theorem: If you have a number $x$ with $n$ number of decimal places and another number $y$ with $l$ number of decimal places, then $x \cdot y$ will never have more than $n + l$ decimal places.

For example:

$63.987 \cdot 56.358 = 3606.179346$ (3 decimal places + 3 decimal places = 6 decimal places)

1) Is this true? Is there a proof?

2) Is there a name for this theory/principle?

(not a homework problem)

So, in your sense, $x$ having $\le 3$ decimal places means $x = K/10^3$ for some natural number $K$. — GEdgar, Jan 24 '14 at 23:22

score 2 · Accepted Answer · answered Jan 24 '14 at 22:03

2

This is a consequence of the basic laws of power arithmetic: $10^x 10^y = 10^{x+y}$.

answered Jan 24 '14 at 22:03

J.R.

17,904

Is there a name for this theorem?

1 Answers1