**Introduction to Subscripts and Superscripts**

Scientists, engineers, and other technical people use *scientific notation* to express the extreme quantitative values they encounter. In real-world applications, trigonometry often involves vast distances and tiny angles that don’t lend themselves very well to expression as ordinary decimal numbers.

Some of the problems so far in this book have involved rounding answers off to a certain number of decimal places. In scientific and engineering work, it is the number of *significant figures,* more than the number of decimal places, that matters. Decimal places and significant figures sometimes mean the same thing, but not always.

*Subscripts* are used to modify the meanings of units, constants, and variables. A subscript is placed to the right of the main character (without spacing) and is set below the base line.

Superscripts almost always represent *exponents* (the raising of a base quantity to a power). Italicized, lowercase English letters from the second half of the alphabet ( *n* through *z* ) denote variable exponents. A superscript is placed to the right of the main character (without spacing) and is set above the base line.

**Examples Of Subscripts**

Numeric subscripts are never italicized, but alphabetic subscripts are if they represent variables. Here are three examples of subscripted quantities:

*θ*_{0}– read “theta sub nought”; stands for a specific angle*R*_{out}– read “*R*sub out”; stands for output resistance in an electronic circuit*y*– read “_{n}*y*sub*n*”; represents a variable with a variable subscript

Ordinary numbers are rarely, if ever, modified with subscripts. You are not likely to see expressions like this:

Constants and variables can come in many “flavors.” Some physical constants are assigned subscripts by convention. An example is *m* _{e} , representing the mass of an electron at rest. (The “e” in this case is not italicized because it stands for the word “electron,” not for a variable or the natural logarithm base.)

Sometimes subscripts are used for convenience. Points in three-dimensional space are sometimes denoted using ordered triples such as ( *x* _{1} , *x* _{2} , *x* _{3} ) rather than *(x,y,z).* This subscripting scheme becomes especially convenient if you’re talking about points in a higher-dimensional space, for example ( *x* _{1} , *x* _{2} , *x* _{3} ,..., *x* _{11} ) in Cartesian 11-dimensional (11D) space.

**Examples Of Superscripts**

Numeric superscripts are never italicized, but alphabetic superscripts usually are. Examples of superscripted quantities are:

- 2
^{3}– read “two cubed”; represents 2 × 2 × 2 - sin
^{2}*θ*– read “the square of the sine of theta”; represents a quantity multiplied by itself - sin
^{–1}*θ*– read “the inverse sine of theta”; alternative expression for arcsin θ

Practice Problems for these concepts can be found at: Scientific Notation Practice Test

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