# Numbers and Operations

## Vocabulary

### exponent

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

### 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

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

### integer

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

### irrational number

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

### natural number

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

### order of operations

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

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

### 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 $\frac{1}{2}$ and $-\frac{2}{3}$

### 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 $1, 2, 3, 4,...$