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# Number Theory Unit

### Terrell-NUMBER THEORY: Terms from the Number Theory Unit (October - November)

Term | Definition | Example |
---|---|---|

NATURAL NUMBERS | The set of all counting numbers beginning with 1. (a.k.a. positive integers) | 1, 2, 3, 4, 5, 6, ... |

WHOLE NUMBERS | The set of all counting numbers beginning with 0. (a.k.a. nonnegative integers) | 0, 1, 2, 3, 4, 5, 6, ... |

INTEGERS | The set of all positive and negative counting numbers, including 0. | ..., -3, -2, -1, 0, 1, 2, 3, ... |

RATIONAL NUMBERS | The set of all numbers that can be expressed as fractions. | .5, -4, 37, 2/9 |

IRRATIONAL NUMBERS | The set of all numbers that cannot be expressed as fractions. | pi, the square root any prime number |

DIVISIBLE | The condition where one natural number divides evenly into another natural number with no remainder. | 56 is divisible by 7, because 7 divides into 56 8 times with no remainder. |

FACTORING | The process of writing a natural number as the product of two or more natural numbers. (The numbers that make up the product are called factors.) | 18 = 3 * 6; 3 and 6 are factors |

PRODUCT | The result of multiplying two or more numbers together. | 3 * 6 = 18; 18 is the product |

PRIME NUMBER | A natural number that has exactly two factors, 1 and itself. | 2, 3, 5, 7, 11, 13, ... |

COMPOSITE NUMBER | A natural number that has three or more factors. | 4, 6, 8, 9, 10, 12, ... |

PRIME FACTORIZATION | The process of expressing a number as the product of all prime numbers. | 28 = 2 * 2 * 7 |

MULTIPLE | The product of a given number and any whole number. | 2 * 1 = 2, 2 * 5 = 10, and 2 * 11 = 22; therefore, 2, 10, and 22 are multiples of 2. |

TERMINATING DECIMALS | Decimals that have a definite number of digits. | 2.4, 6.95, 3 |

REPEATING DECIMALS | Decimals in which one or more digits repeat forever. | .3333...., .70707..., .02999... |

NONREPEATING DECIMALS | Decimals that do not end nor repeat. | square root of any prime number, pi |

POWER | An expression that has base and an exponent. | 2^3, x^-9 |