Metric micro-scale: one micron (micrometre) equals how many centimetres?

Introduction / Context:Unit conversions at micro-scale are essential in filtration, particle technology, microfabrication, and microscopy. Knowing how micrometres relate to centimetres avoids costly specification errors in screens and membranes.

Given Data / Assumptions:

• 1 micrometre (1 micron) = 1 µm = 10^-6 m.
• 1 metre = 100 centimetres = 10^2 cm.

Concept / Approach:Convert micrometres to metres, then metres to centimetres by multiplying by 100. Use exponent rules to simplify the power of 10.

Step-by-Step Solution:Start: 1 µm = 10^-6 m.Convert to cm: 10^-6 m * 100 cm/m = 10^-6 * 10^2 cm.Combine exponents: 10^-4 cm.

Verification / Alternative check:Since 1 cm = 10,000 µm, the reciprocal check gives 1 µm = 1/10,000 cm = 10^-4 cm.

Why Other Options Are Wrong:10^-2 is too large (that is 0.01 cm = 100 µm); 10^-6 is metres, not centimetres; 10^-8 and 10^-5 are inconsistent with the two-step conversion.

Common Pitfalls:Skipping the metre-to-centimetre step or mixing up powers of ten.

Final Answer:10^-4