In units of centimetre, one nanometre (1 nm) is equal to which of the following numerical values?

Introduction / Context:

Nanometre is a very small unit of length widely used in atomic physics, semiconductor technology and nanoscience. Being comfortable with converting nanometres into metres and centimetres helps in understanding orders of magnitude and in comparing sizes at microscopic scales. This question asks you to express one nanometre in terms of centimetre using scientific notation.

Given Data / Assumptions:

• 1 nanometre (1 nm) is defined as 10^-9 metre.
• 1 metre equals 100 centimetre.
• We need to convert 10^-9 metre into centimetre.

Concept / Approach:

First, recall the definitions: 1 nm = 10^-9 m and 1 m = 100 cm = 10^2 cm. To convert nm to cm, we multiply 10^-9 m by 10^2 cm per metre. This gives 10^-9 * 10^2 cm = 10^-7 cm. Hence, one nanometre is equal to 10^-7 centimetre. The other options correspond to different powers of ten and represent much larger lengths than a nanometre.

Step-by-Step Solution:

Verification / Alternative check:

As an alternative, convert everything through metres. Knowing that 1 cm = 10^-2 m, we can write 1 nm / 1 cm = (10^-9 m) / (10^-2 m) = 10^-9 / 10^-2 = 10^(-9 + 2) = 10^-7. This means that one nanometre is 10^-7 of a centimetre, confirming the earlier calculation.

Why Other Options Are Wrong:

Option B: 10^-6 cm corresponds to a length ten times larger than a nanometre.

Option C: 10^-4 cm is much larger still, equal to 1 micrometre (10^-6 m), not a nanometre.

Option D: 10^-3 cm equals 10^-5 m, which is 10 000 times larger than a nanometre.

Common Pitfalls:

Students sometimes mix up micrometre (μm) and nanometre (nm). Remember that 1 μm = 10^-6 m, whereas 1 nm = 10^-9 m, so 1 μm is 1000 nm. Another common error is mishandling powers of ten when converting between metre and centimetre. Always track exponents carefully adding when multiplying powers of ten and subtracting when dividing.

Final Answer:

One nanometre is equal to 10^-7 cm.