One nanometer is equal to

Metric prefixes attach a fixed power-of-ten multiplier to a base unit: nano- (n) multiplies by 10-9, and centi- (c) multiplies by 10-2. Converting a quantity from one metric-prefixed unit to another, both built on the same base unit (metre), means multiplying by the ratio of these two multipliers.

1. By definition, 1 nanometre = 10-9 metre.

2. By definition, 1 metre = 102 centimetre (since centi- = 10-2 metre, one metre contains 102 centimetres).

3. Substituting, 1 nanometre = 10-9 × 102 centimetre = 10-7 centimetre (adding the exponents: -9 + 2 = -7).

Independently, chaining the conversion through the metre confirms this: 10-9 m × (102 cm / 1 m) = 10-7 cm, which matches only the 10-7 cm option among those offered.

Hence, 1 nanometre = 10-7 cm.