Change the decimals to whole numbers with powers.
Count how many numbers are after the decimal points and express the whole number to 10 raise to the power of the negative of that number
0.5445
There are 4 numbers after the decimal points thus 5,4,4 and 5
0.5445=5445×10−40.09
There are two numbers after the decimal points, thus 0 and 9
0.09=9×10−29 goes into 5445,605 times and itself once
Apply the law of indices to simplify the powers
Since base 10 in each of the indices, we can apply the low of indices
Thus if the bases are the same and dividing, you subtract the power of the denominator from the power of the numerator
NOTE: to change the result back to decimal, you move the decimal points as many times as the negative power to the left
Every whole number has a decimal point at the end. Hence
605=605.0Since the power is negative
2(−2), we move the decimal point to the left 2 times, landing after 6