Transcript 8th Grade Math SCOS

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8
Grade Math SCOS
Goal 1: Numbers & Operations
J. Grossman
Vobabulary
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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.
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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.
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Their decimal representations neither terminate nor repeat. Ex. √3, pi ,
0.14114111411114…
The Real Numbers
Radicals
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Radicals (or "roots”) are the
"opposite" operation of applying
exponents; you can "undo" a power
with a radical.
• The symbol is √
Radicals
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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
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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
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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
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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
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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
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Examples of Repeating Decimals:
Decimals
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Decimals that repeat/do not
terminate or decimals that terminate
are rational numbers.
They can be converted to some
fractional equivalent.
Decimals
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Non-repeating Decimal:
• A decimal that never repeats itself. For
example, pi is a non-repeating decimal.
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Non-terminating Decimal:
• A decimal that never ends or never
terminates.
Decimals
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Decimals that do not repeat and do
not terminate are irrational numbers.
They cannot be converted to some
fractional equivalent.
Estimation vs. Approximation
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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… ???