Rules for Powers of 10

Multiplication:
Powers of 10 greater than 1 (10, 100, 1000.......)
Number will become larger.  Move decimal to the right the same number of places as zeros in the power of 10
5.78 x 100 = 57810   2 places

Powers of 10 less than 1 (0.1, 0.01, 0.001......)
Number will always become smaller.  Move decimal to the left the same number of places as decimal places in the power of 10.
5.78 x 0.01 = 0.0578   2 places

Division:
Powers of 10 greater than 1(10, 100, 1000)
Number will become smaller.  Move decimal to the left the same number of places as zeros in the power of 10.
78.6 ÷ 10 = 7.86   1 place

Powers of 10 less than 1 (0.1, 0.01, 0.001)
Number will become larger.  Move decimal to the right the same number of places as decimal places in the power of 10.
78.6 ÷ 0.1 = 786    1 place