The digits stay the same. The decimal point hops one place for each zero: right to multiply, left to divide.
3.45
Watch the point hop, then see the digits slide into their new places.
Multiply: the point hops right, one place for each zero.
Divide: the point hops left, one place for each zero.
An empty place gets a 0, so the point has somewhere to land.
A whole number has a hidden point after its ones digit.
The digits never change order. Really they slide: each one is worth 10 times more or less.
Move the decimal point one place to the right for each zero: once for 10, twice for 100, three times for 1000. So 3.45 × 100 = 345. If you run out of digits, fill the empty places with zeros: 2.5 × 1000 = 2500.
Move the decimal point one place to the left for each zero. So 56 ÷ 100 = 0.56 and 4.2 ÷ 1000 = 0.0042. When nothing is left in front of the point, write a 0 there.
Both give the same answer. On a place value chart the digits slide one column left when you multiply by 10, because each is worth ten times more, while the point stays put. Hopping the point the other way is a quicker way to see the same thing. The Try it level shows both: the point hops, then the digits slide under their new columns.
Whole numbers by 10 and 100 come at about 8 or 9. Decimals by 10, 100 and 1000 follow at about 10 or 11, and the same idea is used again to convert units such as metres and centimetres.