Explain the relationship between multiplying and diving by 10, 100, and 1,000 and moving the decimal point to the right or to the left.

If you're multiplying by 10, you're moving the decimal point to the right, the same with any multiplication in the 10's, so 100, 1,000, etc. This is because you are making the number 10 times larger, so if you had 3.4, the 4 is in the 1/10 column so multiplying by 10 would put it in the units column, making the number 34.

On the other hand, dividing by the 10's makes the decimal point move to the left because you are making the number 10 times smaller, so if the units column is worth 1, then 10 times less than that is 1/10, which is the first decimal place.

I hope this helps! I tried to explain it well but let me know if you still don't understand or if I've confused you in any way :)

Absolute value graph shifted point 5 up