Numbers and Operations

Vocabulary

exponent

number that indicates how many times a base is multiplied by itself; shown by a raised number, such as:
43=4444^3=4\cdot4\cdot4

grouping symbols

symbols, such as parentheses ()(\; ), brackets [][ \;], and braces {}\lbrace\;\rbrace, that are used to separate a part of an expression. Some operation symbols, such as fraction bars and radicals, may also function as grouping symbols.

index

nn in the radical xn\sqrt[n]{x}, which represents the nnth root of xx. For example, the index of x3\sqrt[3]{x} is 3. In the radical x\sqrt{x}, the index is not shown, but it is understood to be 2.

integer

number in the set of whole numbers and their opposites: ...3,2,1,0,1,2,3,......-\!3,-2,-1,0,1,2,3 ,...

irrational number

number in the set of nonterminating, nonrepeating decimals, such as 2\sqrt{2} or π\pi

natural number

number in the set of counting numbers: 1,2,3,4,...1,2,3,4,...

order of operations

set of rules indicating which calculations to perform first to simplify a mathematical expression

radical symbol

symbol 0\sqrt{\phantom{0}} used to represent nnth roots, where nn is a natural number greater than or equal to 2

radicand

expression under a radical

rational exponent

exponent that is a rational number

rational number

number in the set that can be written as a fraction of two integers where the denominator is not zero, such as 12\frac{1}{2} and 23-\frac{2}{3}

rationalizing the denominator

rewriting a fraction to remove radical expressions from the denominator

real number

number in the set of all rational and irrational numbers

scientific notation

notation used to express a number as the product of two factors. The first is a number greater than or equal to 1 and less than 10, and the second is a power of 10.

whole number

number in the set that includes zero and the counting numbers 1,2,3,4,...1, 2, 3, 4,...