Final answer:
Moving the decimal to the right when multiplying by 10 increases each digit's value tenfold, while moving the decimal to the left when multiplying by 0.1 reduces the value tenfold. Zeros serve as placeholders when there aren't enough digits. Scientific notation with powers of ten simplifies multiplication and division of large or small numbers.
Step-by-step explanation:
When multipliying a number by 10, the decimal point is moved to the right because you are increasing the value of each digit by a factor of 10. This is equivalent to moving from a smaller unit to a larger unit. Conversely, when multiplaying a number by 0.1, which is the same as dividing by 10, you must move the decimal point to the left, making each digit ten times smaller. In both cases, we can use zeros as placeholders when there are not enough digits to move the decimal the required number of places.
For example, when multiplying 2.4 by 100, we move the decimal point two places to the right to obtain 240. When converting measurements, such as millimeters to centimeters, we also apply this rule to move the decimal point to the left, reflecting the change from a smaller to a larger unit.
Scientific notation simplifies this process, especially with very large or very small numbers. Multiplying and dividing by tens becomes straightforward when using powers of ten; to multiply two powers of ten, you add the exponents, and to divide, you subtract the exponents.
Overall, this system of moving the decimal point helps to quickly and efficiently perform calculations involving powers of ten without resorting to lengthier multiplication or division processes.