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8 th Grade Math SCOS Goal 1: Numbers & Operations J. Grossman

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Vobabulary Real Numbers: 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…

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The Real Numbers

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Radicals Radicals (or "roots”) are the "opposite" operation of applying exponents; you can "undo" a power with a radical. Radicals (or "roots”) are the "opposite" operation of applying exponents; you can "undo" a power with a radical. exponents The symbol is √The symbol is √

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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: 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:

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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. 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.

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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. 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.integer squareinteger square 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. 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.non-negativesquare rootnon-negativesquare root

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Decimals Terminating Decimals: Terminating Decimals: The word “terminate” means “end”.The word “terminate” means “end”. A decimal that ends is a terminating decimal.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.In other words, a terminating decimal doesn’t keep going. A terminating decimal will have a finite number of digits after the decimal point.

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Decimals Examples of Terminating Decimals: Examples of Terminating Decimals:

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Decimals Repeating Decimal: Repeating Decimal: Also known as a recurring 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.A decimal in which after a certain point a particular digit or sequence of digits repeats itself indefinitely.

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Decimals Examples of Repeating Decimals: Examples of Repeating Decimals:

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Decimals Decimals that repeat/do not terminate or decimals that terminate are rational numbers. Decimals that repeat/do not terminate or decimals that terminate are rational numbers. They can be converted to some fractional equivalent. They can be converted to some fractional equivalent.

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Decimals Non-repeating Decimal: Non-repeating Decimal: A decimal that never repeats itself. For example, pi is a non-repeating decimal.A decimal that never repeats itself. For example, pi is a non-repeating decimal. Non-terminating Decimal: Non-terminating Decimal: A decimal that never ends or never terminates.A decimal that never ends or never terminates.

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Decimals Decimals that do not repeat and do not terminate are irrational numbers. Decimals that do not repeat and do not terminate are irrational numbers. They cannot be converted to some fractional equivalent. They cannot be converted to some fractional equivalent.

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Estimation vs. Approximation Estimation: finding a value that is close enough to the right answer, usually with some thought or calculation involved. 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. Approximation: finding a value that is not exact, but close enough to be used. It is usually a decimal approximation using a rounding method.It is usually a decimal approximation using a rounding method. Round to the nearest 10 th, 100 th, integer value, etc. Round to the nearest 10 th, 100 th, integer value, etc.

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