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Expressing Multiplication and Division 

Expressing Multiplication and Division

Mathematical Composition

Stephen J. Lurie

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Expressing Multiplication and Division

The product of 2 or more terms, including units of measure, is conventionally indicated by a raised multiplication dot (·) (eg, 7 kg · m2) or by 2 or more characters closed up (eg, y = mx + b). However, in scientific notation the times sign (×) is used (eg, 3 × 10−10 cm) (see 18.4.4, Units of Measure, Use of Numerals With Units, Multiplication of Numbers). An asterisk should not be used to represent multiplication, despite its use in this role in computer programs. Note: However, there may be occasions on which the asterisk may be used to provide the reader with the exact equation used in the analysis (eg, regression models).

A forward slash, a horizontal line, a negative exponent, or the word per may be used to express rates, which are generally obtained by dividing one unit by another. For example, velocity (meters per second) may be expressed as


Complex rates involve division of a rate by another unit. Complex rates that are used frequently are conventionally indicated by 2 slashes in the same expression, eg:

The dose was 25 mg/kg/d.

Plasma renin activity was 1.3 ng/mL/h.

Acceleration at the surface of the earth is 9.8 m/s/s (or 9.8 m/s2).

Most complex rates, however, are developed for particular applications. For clarity, these less commonly used rates should be expressed as “a/b per c.” For instance,

The infusion was 2 mL/kg per minute.

Negative exponents may also be used to express such a rate when appropriate: 2 mL·Kg−1·min−1 (see 18.2.2, Units of Measure, Expressing Unit Names and Symbols, Products and Quotients of Unit Symbols). Common sense and clarity should guide this decision.

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