* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download 8th Grade Math SCOS
Survey
Document related concepts
Georg Cantor's first set theory article wikipedia , lookup
Law of large numbers wikipedia , lookup
Mathematics of radio engineering wikipedia , lookup
Infinitesimal wikipedia , lookup
History of logarithms wikipedia , lookup
Proofs of Fermat's little theorem wikipedia , lookup
Large numbers wikipedia , lookup
Real number wikipedia , lookup
Location arithmetic wikipedia , lookup
Approximations of π wikipedia , lookup
Transcript
th 8 Grade Math SCOS Goal 1: Numbers & Operations J. Grossman Vobabulary Real Numbers: the set of rational and irrational numbers. • Natural numbers: the counting numbers: {1,2,3… } • Whole numbers: the set of counting numbers plus zero:{0,1,2,3,..} • Integers: the set of counting numbers and their opposites plus zero {… -3,2,-1, 0, 1, 2, 3… } • Rational numbers: numbers that can be expressed as the ratio of two integers. Decimal representations of rational numbers either terminate or repeat. Ex. 2.375 , 4, -.25, -.14 • Irrational numbers: numbers that cannot be expressed as a ratio of two integers. Their decimal representations neither terminate nor repeat. Ex. √3, pi , 0.14114111411114… The Real Numbers Radicals Radicals (or "roots”) are the "opposite" operation of applying exponents; you can "undo" a power with a radical. • The symbol is √ Radicals For instance, if you square 2, you get 4, and if you "take the square root of 4", you get 2; if you square 3, you get 9, and if you "take the square root of 9", you get 3: Radicand The radicand is the value inside the radical sign. It is the value you want to take the root of. In √x, "x" is the radicand. Perfect Square A square number, sometimes also called a perfect square, is an integer that is the square of an integer; in other words, it is the product of some integer with itself. For example, 9 is a square number, since it can be written as 3 × 3. Square numbers are non-negative. Another way of saying that a (non-negative) number is a square number, is that its square root is again an integer. For example, √9 = 3, so 9 is a square number. Decimals Terminating Decimals: • The word “terminate” means “end”. • A decimal that ends is a terminating decimal. • In other words, a terminating decimal doesn’t keep going. A terminating decimal will have a finite number of digits after the decimal point. Decimals Examples of Terminating Decimals: Decimals Repeating Decimal: • Also known as a recurring decimal; • A decimal in which after a certain point a particular digit or sequence of digits repeats itself indefinitely. Decimals Examples of Repeating Decimals: Decimals Decimals that repeat/do not terminate or decimals that terminate are rational numbers. They can be converted to some fractional equivalent. Decimals Non-repeating Decimal: • A decimal that never repeats itself. For example, pi is a non-repeating decimal. Non-terminating Decimal: • A decimal that never ends or never terminates. Decimals Decimals that do not repeat and do not terminate are irrational numbers. They cannot be converted to some fractional equivalent. Estimation vs. Approximation Estimation: finding a value that is close enough to the right answer, usually with some thought or calculation involved. Approximation: finding a value that is not exact, but close enough to be used. • It is usually a decimal approximation using a rounding method. Round to the nearest 10th, 100th, integer value, etc. Any questions… ???