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Nano- (Prefix) — Definition, Formula & Examples

Nano- is a metric prefix meaning one billionth, or 10−910^{-9}. It tells you to divide the base unit by 1,000,000,000.

The SI prefix nano- (symbol: n) denotes a factor of 10−910^{-9}, equal to 0.0000000010.000000001 of the base unit. It is used in the International System of Units to express quantities one billion times smaller than the reference unit.

Key Formula

1 n(unit)=10−9 (unit)1 \text{ n(unit)} = 10^{-9} \text{ (unit)}
Where:
  • n\text{n} = The nano- prefix, representing a factor of one billionth
  • unit\text{unit} = Any SI base or derived unit (meter, second, gram, etc.)

How It Works

When you see nano- attached to a unit, multiply the number by 10−910^{-9} to convert to the base unit. For example, 5 nanometers means 5×10−95 \times 10^{-9} meters. To go the other direction, divide the base-unit value by 10−910^{-9} (or multiply by 10910^{9}) to get the nano- value. The prefix is commonly seen in nanometers (nm), nanoseconds (ns), and nanograms (ng).

Worked Example

Problem: A strand of DNA is about 2.5 nanometers wide. Express this width in meters.
Write the conversion factor: One nanometer equals 10−910^{-9} meters.
1 nm=10−9 m1 \text{ nm} = 10^{-9} \text{ m}
Multiply: Multiply 2.5 by the conversion factor.
2.5 nm=2.5×10−9 m2.5 \text{ nm} = 2.5 \times 10^{-9} \text{ m}
Answer: The DNA strand is 2.5×10−92.5 \times 10^{-9} meters, or 0.00000000250.0000000025 m, wide.

Why It Matters

Nano- appears constantly in science classes when discussing wavelengths of light (400–700 nm), cell biology, and computer chip sizes. Understanding metric prefixes lets you move between scales quickly, which is essential in physics, chemistry, and engineering courses.

Common Mistakes

Mistake: Confusing nano- (10−910^{-9}) with micro- (10−610^{-6}).
Correction: Remember that nano- is 1,000 times smaller than micro-. A quick check: nano- has 9 zeros after the decimal point, micro- has 6.