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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 |