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math vocab

8th grade vocabulary

real numbers made up of two sets of two numbers- rational/irrational. can be written as fractions, mixed numbers, decimals, positive and negative numbers, and radicals. ex; 1/2, 5 3/4, 2.33..., 1.5, 4, 0, -6, √2
rational numbers consists of integers, terminating/repeating decimals. all rational numbers can be expressed as a fraction. 8 5/6 = 8.833..., .5 = 1/2, .99..., -3,-2,-1,0,1,2,3...
integers all natural numbers, their opposites, and zero. doesn't include fractions/decimals. all whole numbers. (-3,-2,-1,0,1,2,3,4...)
whole numbers consists of natural numbers and zero. (0,1,2,3,4...)
natural numbers are all counting numbers. ex; (1,2,3,4...)
irrational numbers all numbers that are non-terminating/non-terminating decimals; cannot be expressed as a fraction. ex; pi, √47, √2
real number system made of rational and irrational numbers. 5 subsets; rational, integers, whole numbers, natural numbers, irrational
radical a symbol that expressed a square root, a cube root, etc. ex; √64
perfect squares product of an integer multiplied by itself. ex; 2^2 = 4, 3^3 = 9, etc.
exponential notation a method of rewriting numbers- number is a base raised to an exponent. ex; 2^3 x 5^4
exponent a number to which the base is not raised ex; exp. of 7^3 would be 3
power product of repeated multiplication of the same factor. ex; power of 10^8 = 100,000,000
base factor that is multiplied. ex; base of 7^3 would be 7
prime factorization a number written as a product of its prime numbers. ex; 81 = 9 x 9 = 3 x 3 x3 x 3 = 3^4
product of power property when the product of two exponential notations have the same base, you add the exponents. ex; 10^4 x 10^3 = 10^4+3 = 10^7
quotient of power property when the quotient of two exponential notations have the same base, subtract the exponents. ex; 10^4 /10^3 = 10^4-3 = 10^1 = 10
power to a power property take an expression that is always raised to an exponent and raised to another exponent. ex; (2^3)^4 = 2^3 x 2^3 x 2^3 x 2^3 = 2^12
power of a product property different bases, same exponents. combine bases in parentheses and raise it to the same exponent. ex; 4^3 x 5^3 = (4 x 5)^3 = 20^3
product of quotient property different bases, same exponent. combine bases in parentheses and raise to same exponent. ex; 2^3/3^3 = (2/3)^3
zero exponents states that any term w/ an exponent of zero is equal to one ex; 3° = 1
negative exponents exponents that are negative- write them as positive ex; x^-6 = 1/x^6