University Physics Volume 1 — Mechanics · Problem 26

Units and Measurement — OpenStax

Physics — University · units-and-standards

Problem

The following lengths are given using metric prefixes on the base SI unit of length: the meter. Rewrite them in scientific notation without the prefix. For example, 4.2 Pm would be rewritten as 4.2×10154.2 \times 10^{15} m. (a) 89 Tm; (b) 89 pm; (c) 711 mm; (d) 0.45 μ\mum.
Intuitive explanation

Metric prefixes are just shorthand for powers of 10—each prefix represents a fixed multiplier you multiply by the base unit. To convert, replace the prefix with its corresponding power of 10, then express the whole number in scientific notation. The key is memorizing (or looking up) what each prefix means: T is 101210^{12}, p is 10−1210^{-12}, m is 10−310^{-3}, and μ\mu is 10−610^{-6}.

Intuitive explanation

Metric prefixes are just shorthand for powers of 10—each prefix represents a fixed multiplier you multiply by the base unit. To convert, replace the prefix with its corresponding power of 10, then express the whole number in scientific notation. The key is memorizing (or looking up) what each prefix means: T is 101210^{12}, p is 10−1210^{-12}, m is 10−310^{-3}, and μ\mu is 10−610^{-6}.

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