Metric prefixes — scale comparison: Pico (p) compared to micro (μ) represents what numerical relation?

Introduction / Context:
Metric prefixes compactly encode powers of ten, enabling quick reasoning across scales in electronics and science. Comparing pico and micro matters when converting capacitances (pF vs μF), currents (pA vs μA), or times (ps vs μs). Misconversions can cause six-orders-of-magnitude errors, which are catastrophic in design and data reporting.

Given Data / Assumptions:

• Pico (p) = 10^−12.
• Micro (μ) = 10^−6.
• We seek pico as a fraction of micro.

Concept / Approach:

The ratio is computed by dividing the two powers of ten. If quantity X_pico equals 10^−12 and X_micro equals 10^−6, then X_pico / X_micro = 10^−12 / 10^−6 = 10^−6, meaning pico is one-millionth of micro. The same relation holds across any base units (farads, seconds, amps).

Step-by-Step Solution:

Verification / Alternative check:

Cross-check with common conversions: 1 μF = 10^−6 F; 1 pF = 10^−12 F. Dividing confirms the million-to-one relationship. Many capacitor datasheets list both units, reinforcing this conversion.

Why Other Options Are Wrong:

• one-tenth / one-hundredth / one-thousandth: These represent 10^−1, 10^−2, 10^−3, far larger than 10^−6.
• one-billionth: 10^−9, not the correct ratio between pico and micro.

Common Pitfalls:

• Mistaking milli (10^−3), micro (10^−6), nano (10^−9), and pico (10^−12) order.
• Dropping zeros when converting, leading to significant magnitude errors.

Final Answer:

one-millionth