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# FOA 2 Unit 1

### Number Theory: real numbers system, exponents, scientific notation, properties

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

Real Numbers | all the numbers we use every day |

Rational Numbers | any number that can be written as a fraction (ratio); any decimal that terminates (ends) or repeats |

Integers | whole numbers (0, 1, 2, 3, 4, ...) and their opposites (-1, -2, -3, ...) |

Whole Numbers | 0, 1, 2, 3, 4, ... |

Natural Numbers | 1, 2, 3, 4, 5, ... |

Irrational Numbers | decimals that are non-terminating and non-repeating; non-perfect squares, pi |

How do I handle a negative exponent? | flip the base over the fraction bar and change the exponent sign to positive |

What is the base of an exponent? | the large number written on the line; the number that gets multiplied by itself |

What is the power of an exponent? | the little number that is written next to the base; it means how many times the base is multiplied by itself |

What is a radical sign? | the symbol that means square root |

Perfect Square | the number you get when you square a whole number (ex. 10 squared = 100; 100 is a perfect square) |

Scientific Notation | the method of writing numbers in terms of a decimal number between 1 and 10 multiplied by a power of 10 |

Standard Notation | our normal way of writing numbers |

Commutative Property of Addition | a + b = b + a; 3 + 4 = 4 + 3 |

Commutative Property of Multiplication | a * b = b * a; 5 * 6 = 6 * 5 |

Associative Property of Addition | a + (b + c) = (a + b) + c 1 + (2 + 3) = (1 + 2) + 3 |

Associative Property of Multiplication | (a * b) * c = a * (b * c) (4 * 5) * 6 = 4 * (5 * 6) |

Distributive Property | a(b + c) = a*b + a*c 2(3 + 4) = 2*3 + 2*4 |

Additive Identity Property | a + 0 = a; 9 + 0 = 9 |

Multiplicative Identity Property | a * 1 = a; 9 * 1 = 9 |

Additive Inverse Property | a + (-a) = 0; 4 + (-4) = 0 |

Multiplicative Inverse Property | a * 1/a = 1; 3 * 1/3 = 1 |

Multiplication of Zero Property | a * 0 = 0; 7 * 0 = 0 |

Created by:
MrsCMath7