Slide the digits
Press ×10 and every digit slides one column to the left. Press ÷10 and every digit slides one column to the right. The orange decimal point never moves. Type your own number to start with, then try ×100 and ÷100.
Try this. Start with 0.07. Which one button turns it into 7? Decide first, then press it.
Answer
×100. The 7 has to slide two columns to the left, from the hundredths column to the ones column. Each column is worth ten times more than the one before, and 10 × 10 = 100.
What's going on
Each column is worth ten times the column on its right. Ten ones make a ten. Ten tens make a hundred. It works past the decimal point too: ten tenths make a one, and ten hundredths make a tenth.
So to make a number ten times bigger, you do not need to calculate. Move every digit one column to the left, and each digit is now worth ten times what it was. To make it ten times smaller, move every digit one column to the right.
The pale zeros are place holders. They fill the empty columns so you can tell 3 from 30 and 0.3 from 0.03.
People sometimes say "add a zero to multiply by 10". Try it on 3.45 and see why that rule lets you down: 3.450 is the same number as 3.45. Sliding the digits always works.