Read/Write to Trillions 2,156,037,008,129 is read as: Two trillion, one hundred fifty-six billion, thirty-seven million, eight thousand, one hundred twenty-nine. Sixty-four million, two hundred six thousand, eleven is written as: 64,206,011

Estimation and Rounding Estimate – An answer that is an approximation Round a number – To approximate the value of a whole number to a specific place value using specific rules Underline the place value to be rounded to Circle the number to the right The underlined digit remains the same if the circled number is 1,2,3, or 4 The underlined digit rounds up if the circled number is 5,6,7,8 or 9 Round to the nearest 10: 125= =120

Exponents Exponent - Tells how many times a number is used as a factor. (b^a a = exponent) Power - A verbal expression of a number with an exponent. (3^8 is a power) Exponential Form – A number written using exponents. (32 = 2^5) Base - A number that is raised to an exponent. (b^a b = base) Evaluate - To find the value of a mathematical expression. Expression – A mathematical representation containing numbers, variables, and operating symbols; an expression does not include an equality or inequality symbol. (27 / 3)

Exponents cont. 4 * 4 * 4 * 4* 4 = 4^5 3^6 = 3 * 3 * 3 * 3 * 3 * 3 The expression 3^8 is read as “3 to the 8 th power or 3 to the power of 8”. 4^2 = Four raised to the 2 nd power or 4 squared. 4^3 = Four raised to the 3 rd power or four cubed. 5 ^ 1 = 5 5 ^ 2 = 25 5 ^ 3 = 125

Order of Operations Operations – Procedures used to combine numbers, expressions, or polynomials into a single result. Please Excuse My Dear Aunt Sally (PEMDAS) 1) Parentheses 2) Exponents 3) Multiply or Divide in order from left to right (whichever comes first) 4) Add or Subtract in order from left to right (whichever comes first) Examples: 3 * (2 + 6) / 2^ / 2 – 5 * 7

Base Ten Number system – A place value number system in which ten digits, 0 through 9, are used to represent a number and the value of each place is 10 times the value of the place to its right; the value of any digit in the number is the product of that digit and its place value. Counting/Natural numbers – All whole numbers greater than zero. Whole numbers – The set of counting numbers plus zero.

Associative Property of Addition A property of real numbers that states that the sum of a set of numbers is the same, regardless of how the numbers are grouped. 2 + (3 + 7) = (2 + 3) + 7 Associative Property of Multiplication A property of real numbers that states that the product of a set of numbers is the same, regardless of how the numbers are grouped. 6 * (8 * 7) = (6 * 8) * 7

Commutative Property of AdditionCommutative Property of Addition Commutative Property of Multiplication A property of real numbers that states that the sum of two terms is unaffected by the order in which the terms are added; i.e., the sum remains the same. a + b = b + a Commutative Property of Multiplication A property of real numbers that states that the product of two factors is unaffected by the order in which they are multiplied; i.e., the product remains the same. a * b = b * a

Distributive property of multiplication over addition A property of real numbers that states that the product of the sum of two numbers is the same as the sum of their products. A property of real numbers that states that the product of the sum of two numbers is the same as the sum of their products. 2(15 + 4) = 2 * * 4 2(15 + 4) = 2 * * 4 Properties of real numbers – Rules that apply to the operations with real numbers.

Identity Property of Addition & Subtration Identity Property of Addition & Subtration A set of numbers where any number n, added to zero(0) will result in the number n, the identity element for addition and subtraction is the number zero(0). Identity Property of Multiplication & Division A set of numbers where any number n, multiplied by one(1) will result in the number n, the identity element for multiplication and division is the number one(1). Zero property of Multiplication – The property that states that the product of any number and zero is always zero a * 0 = 0 for all a

Inverse Operations Inverse operation of addition – An operation that is the opposite of, or undoes, another operation; addition and subtraction are inverse operations. Inverse operation of division - An operation that is the opposite of, or undoes, another operation; multiplication and division are inverse operations.