Chapter 1 - Numbers Flashcards
What are factors
#s that divide EVENLY into a larger # Eg. 24 - 1,2,3,4,6,8,12,24
Prime Number
A whole # which has exactly 2 factors. - 1 and it’s self
Eg. 3 & 7
Composite Number
A whole number which has more than 2 factors
Eg. 10 & 21
What are 1 and 0
1 is neither a prime or a composite
0 has no factors
First 10 primes
2,3,5,7,11,13,17,19,23,25…
Prime factors
A whole number are the factors of the number which are prime
Eg. Prime factors of 6 - 2, 3
Prime Factorization
Expressing a whole number a a product of primes
Eg. Division table or tree diagram
Greatest Conmon Factor
GCF
Largest whole number which divides exactly into each of the members of the set
Lowest Common Multiple
LCM
The lowest quantity that is a multiple of two or more given quantities (e.g. 12 is the lowest common multiple of 2, 3, and 4).
Perfect square
Whole numbers that can be divide into one number.
Eg. 1,2,4,9,16,25,36,49…
Square Roots
One positive and one negative
Even numbers ONLY have a positive
Principal Square Roots
ONLY the positive square root
Square root symbol only looking for positive answers
Perfect Cube
A number that can be divided into another number 3 times
Eg. 1,8,27,64,125
Cube root
The number that multiplied by its 3 time s equals another number
Eg. 1,2,3,4,5…
Repeating Decimal
Decimals which have a recurring pattern of digits
Non-Repeating Decimals
Decimals which have no recurring pattern of digits
Terminating Decimal
Decimals with a finite number of digits
Non-Terminating
Decimals with an infinite number of digits
Rational numbers (Q)
Decimal numbers that repeat or terminate. They can be converted into fractions
a/b where a,b are integers b≠0
Irrational Numbers (Q-)
Decimal numbers which are both non-repaying AND non-terminating. They cannot be converted into fractions
Converting a Repeating Decimal to a Fraction Algebraically
Step 1: let x be the original number
Step 2: identify the repeating digit(s)
Step 3: multiply both sides by a power of ten. The repeating number(s) should be to the left of the decimal.
Step 4: if the repeating number is not on both sides of the decimal multiply both sides by a power of ten so that the repeating number(s) are on the right side of the decimal.
Step 5: subtract the equation in step four from the equation in step 3 or subtract step 3 from the original. Then solve for x.
Real Number System
Real numbers (R) break in to: Rational (Q) and Irrational (Q-). Rational numbers > Integers (I) > Whole Numbers (W) > Natural Numbers (N)
Real Numbers (R)
Any and all numbers that we can get mathematically
Integers (I)
Negative and positive “WHOLE” numbers
