Final answer:
To convert a larger unit to a smaller unit in mathematics, one typically multiplies and moves the decimal point to the right. In contrast, going from a smaller unit to a larger one involves dividing and shifting the decimal point to the left. Scientific notation and powers of ten can be used as shortcuts in this conversion process.
Step-by-step explanation:
When you change a larger unit into a smaller unit, you generally multiply and move the decimal point to the right. This may involve multiplying by 10, 100, 1,000, or 10,000 depending on the units involved. Conversely, when converting from a smaller unit to a larger unit, we divide by those same factors and move the decimal point to the left. If we consider converting centimeters to millimeters, which are smaller units, we multiply by 10. But if we go from millimeters to centimeters, we divide by 10 and thus move the decimal point one place to the left.
Using scientific notation and powers of ten, we can streamline this process. For instance, multiplying a number by 103 (which is 1,000) means moving the decimal three places to the right. Similarly, when dividing by 10-4 (0.0001), we move the decimal four places to the left.
When there aren't enough decimal places to move, we use zeros as placeholders. For example, if we multiply 2.4 by 100, we need to move the decimal point two places to the right, adding a zero to make the result 240.