Real Numbers System and standard properties of real #'s Flashcards
What is a Real Number
numbers that can be found on the number line
What’s an Rational number
a number that can be expressed as the quotient of fraction of 2 integers, a numerator and a nonzero denominator.
What’s an integer
A whole number that’s not a fraction its a positive natural number or a negative integer
3/5 is in what category of the number system?
Rational
√72 is what kind of number?
Irrational
What’s an Irrational number?
A real number that cannot be made by dividing 2 integers. Irrational numbers have decimal expansions that neither terminate nor become periodic. Every transcendental number is irrational.
73 is what kind of number?
A natural number / Whole number
pi is what kind of number?
irrational
-39 is what kind of number?
integer
290/840 is what king of number
rational
what is commutative property?
this applies to real numbers operations when the order of numbers doesn’t affect the result, real numbers are commutative with addition and multiplication
what is associative property?
This applies to real number operations if numbers can be grouped differently and still produce the same result. Real numbers are associative with addition and multiplication, but not with subtraction or division.
(a+b)+c=a+(b+c) is what kind of property?
associative
What is distributive property
when simplifying an expression with parentheses
a(b+c)=a⋅b+a⋅c, or that
(b+c)a=b⋅a+c⋅a. is what kind of property?
distributive
What is identity property
the number or circumstance by which you can perform an operation on a real number and still maintain its original identity.
0 is considered to which property?
identity
a+0=a and a*1=a is what kind of property
identity
What is closure property?
the affect or change of a type number when an operation is performed. Real numbers are considered closed under addition, subtraction, multiplication, and division as performing and of those operations between 2 real numbers will result in another real number.
if A and B are real numbers then a+b is what?
a real number (closure property)
What is the inverse property?
the circumstances in which an operation can be performed on a real number to result in the identity of that operation
a+(−a)=0 and a⋅1a=1 is what property?
inverse
√a= a+b / 2*√b (b is the nearest perfectly squared number such as 2)
how to find square root of prime number
What’s a prime number?
Any whole number greater than 1 that is divisible only by 1 and itself, is defined as a prime number.
2 is considered a ____ number
prime
a^m/n =
n√a^m
What is a constant
every numerical term w/out a variable
What is addition property of equality?
adding the same number to both sides of an equation produces an equivalent equation
What property is this? if a=b then a+c=b+c
Addition property of equality
What’s subtraction property of equality
subtracting the same number from both sides of an equation produces an equivalent equation
multiplication property of equality
multiplying both sides of an equation by the same number produces an equivalent equation
what property is this? if a=b then ac=bc
multiplication property of equality
division property of equality
dividing both sides of an equation by the same number produces an equivalent expression
What property is this? if a=b then
What property is this? if a=b then
What’s a significant digit?
is a digit in a measurement that carries a meaning in the precision of the number.
All nonzero numbers are…
significant
zeros between two other significant numbers are…
significant
zeros on the end of numbers w/ decimals are…
significant
zeros at the end of a number without a desimal are…
not significant
numbers to the left of the first nonzero nuber in a decimal are…
not significant
0.000020 has how many significant digits?
2
