In the International System of Units, one nanometre is equal to how many metres?

Introduction / Context:

This question tests knowledge of metric prefixes and very small length scales. The nanometre is widely used in nanotechnology, semiconductor fabrication, and molecular physics to describe atomic and molecular dimensions. Being comfortable with powers of ten and unit conversions is essential in all branches of science and engineering.

Given Data / Assumptions:

• We are working with standard SI prefixes for length based on the metre.
• The term nanometre uses the prefix nano.
• We need to convert one nanometre into metres using powers of ten.
• Options list various powers of ten in metres.

Concept / Approach:

In the SI system, prefixes represent powers of ten. The prefix nano stands for 10^-9. Thus, one nanometre is 10^-9 of a metre. For comparison, micro is 10^-6, milli is 10^-3, and pico is 10^-12. Remembering the order of these prefixes helps in converting between units. Since the question is specifically about nanometre, we apply the nano factor directly.

Step-by-Step Solution:

Verification / Alternative check:

You can place nano in context with nearby prefixes. A micrometre is 10^-6 m, a nanometre is 10^-9 m, and a picometre is 10^-12 m. Thus, 1 nm is one thousand times smaller than 1 micrometre and one thousand times larger than 1 picometre. In atomic physics, typical atomic diameters are a fraction of a nanometre, which again fits the range implied by 10^-9 m. These cross checks confirm that nano corresponds to 10^-9.

Why Other Options Are Wrong:

• 10^3 m: This equals 1000 metres and corresponds to the prefix kilo, used for kilometre, not nanometre.
• 10^-6 m: This is the micrometre scale and corresponds to the prefix micro, not nano.
• 10^-12 m: This is the picometre scale and corresponds to the prefix pico, smaller than a nanometre.

Common Pitfalls:

Learners may confuse the order of prefixes, especially micro and nano, because both refer to very small lengths. Another error is to misread the negative exponent and treat 10^-9 as 10^9. To avoid confusion, it is helpful to memorise a short list of key prefixes: milli 10^-3, micro 10^-6, nano 10^-9, pico 10^-12, and kilo 10^3. Writing them out in order on a number line of exponents can also reinforce the correct relationships.

Final Answer:

One nanometre is equal to 10^-9 metre.