Final answer:
To divide 0.489807 by 0.081 by hand, multiply both numbers by 100 and then divide, placing the decimal in the quotient above where it is in the dividend. Multiplying or dividing by powers of 10 will move the decimal left or right in the result accordingly.
Step-by-step explanation:
To find the quotient of 0.489807 divided by 0.081 by hand, you need to understand how to deal with decimals in division. The first step is to convert the divisor (0.081) into a whole number by multiplying both the divisor and the dividend (0.489807) by the same power of 10. In this case, since the divisor has two decimal places, we multiply both numbers by 100, turning the equation into 48.9807 divided by 8.1.
Now that we have whole numbers, we can place the decimal in the quotient directly above where the decimal appears in the dividend. To divide, we start by seeing how many times the divisor can fit into the initial digits of the dividend. This process is continued until we have divided all the digits of the dividend, including any remainder as necessary.
It's important to know where to place the decimal in the quotient. If you multiply or divide by power of 10, you move the decimal the appropriate number of places to the left or right. For example, when multiplying 1.9436 by 10, it becomes 19.436 - you move the decimal one place to the right. For division, 1.9436 divided by 1000 equals 0.0019436, where the decimal moves three places to the left. This principle helps you to determine the placement of the decimal in any quotient.