Times 10, 100, 1000

Multiplying by 10 makes every digit worth ten times more: tenths become ones, and ones become tens. On paper it looks like the decimal point moving one place to the right. $4.7\cdot 10$ is 47.

100 is 10 times 10, so the point moves two places, and 1000 moves it three: one place for each zero. $0.62\cdot 100$ is 62. When the digits run out, fill with zeros: $1.5\cdot 1000$ is 1500, because the point moves past the 5 and then two more places.

The digits shifting left into bigger places and the point shifting right are the same event seen two ways. It is why money converts so easily: 0.85 of a dollar is 85 cents, since a dollar is 100 cents and the point moves two places.