How do the prefixes in the metric system relate to the basic units?

In the metric system, prefixes are used to denote multiples or fractions of the basic units. Here's how they relate:

1. Kilo- (k): Denotes a factor of 1000. For example, 1 kilometer (km) is equal to 1000 meters (m).

2. Hecto- (h): Denotes a factor of 100. For example, 1 hectometer (hm) is equal to 100 meters.

3. Deca- (da): Denotes a factor of 10. For example, 1 decameter (dam) is equal to 10 meters.

4. Deci- (d): Denotes a factor of 0.1 (1/10). For example, 1 decimeter (dm) is equal to 0.1 meter.

5. Centi- (c): Denotes a factor of 0.01 (1/100). For example, 1 centimeter (cm) is equal to 0.01 meter.

6. Milli- (m): Denotes a factor of 0.001 (1/1000). For example, 1 millimeter (mm) is equal to 0.001 meter.

7. Micro- (µ): Denotes a factor of 0.000001 (1/1,000,000). For example, 1 micrometer (µm) is equal to 0.000001 meter.

8. Nano- (n): Denotes a factor of 0.000000001 (1/1,000,000,000). For example, 1 nanometer (nm) is equal to 0.000000001 meter.

These prefixes allow for easy conversion between different units within the metric system by simply multiplying or dividing by powers of 10.