Final answer:
The reason for the response being off by a multiple of ten is due to the concept of powers of ten. When multiplying or dividing by powers of ten, the decimal point can be moved to the right or left by the number of zeros in the power of ten.
Step-by-step explanation:
The reason for your response being off by a multiple of ten is because of the concept of powers of ten. In our numbering system, each place is ten times greater than the place to the right of it. When multiplying or dividing by powers of ten, we can move the decimal point to the right or left by the number of zeros in the power of ten.
For example, if we multiply 7,000 by 10,000, we are essentially multiplying it by 10⁴. This would mean moving the decimal point four places to the right, resulting in 70,000,000. Similarly, if we divide 70,000,000 by 10,000, we can move the decimal point four places to the left, giving us 7,000.