(8th Grade) Unit 1 Concept Map
LT 1A.1 - 1A.4
LT 1.C.1 - LT 1.C.1
LT 1.B.1 - LT 1.B.2.2
LT 1.A.1
Rational Numbers are numbers that are written as a ratio of two integers and does not repeat. In simple terms it can be written as a fraction
Repeating Decimals i.e irrational numbers are numbers that go on forever and cannot be turned into a fraction
ex: 5/8 8 divided by 5.0 minus 48 equals 20 minus 16 equals 40 minus 40 equals 0. Answer is 0.625
LT 1A.2 Square Roots
A square root is a number multiplied by itself.
Example: 5^2=25, so 5 is a square root of 25
If x^2=y then x is the square root of y
LT 1.A.3
The square root of -25 is not a real number!
Cube root of -4 however is a real number it is -2
imaginary number: square root of -4
LT 1.A.4
Some square roots are irrational
Some are rational
Square root of 36 is Rational
Square root of 100 is Rational
Square root of 10 is irrational
Square root of -7 is irrational
LT 1.B.1
Powers are numbers multiplied by itself. Example: 5x5x5=125 5^3
Forms of exponents: 2^3 Exponent. 2x2x2 Expanded. 8 Standard
DO NOT MULTIPLY EXPONENTS WHEN BASE IS THE SAME!!!!!!
LT 1.B.2
Product of Powers: To multiply powers with the same base: add the exponents
Example: 2^4x2^3 equals 2^4+3=2^7 a^m times a^n equals a^m+n
Monomials are numbers or variables product of a number and one or more variables
2^4 times 2^3 equals (2 times 2 times 2 times 2) times (2 times 2 times 2 ) or 2^7
Notice: the sum of the original exponents is the exponent in the final product!
Quotient of Powers: To divide with the same base, Subtract their exponents
Example: (3^7 divided by 3^7) equals 3^7-3 equals 3^4
(12w^5 divided by 2w) equals (12 over 2)(w^5 over w^3)
DO THE MIDDLE STEP!!!!
LT 1.B.2.2?
Power of a Power: To find a power of a power: MULTIPLY THE EXACT EXPONENTS
Example: (5^2)3 equals 5^2 times 3 equals 5^6 (a^m)n equals a^m times n
(6^4)^5 equals (6^4)(6^4)(6^4)(6^4)(6^4) equals 6^4+4+4+4+4 equals 6^20
LT 1C.1
Scientific Notation is when a number is written as the product of a factor and an integer power of 10. The factor must be greater than or equal to 1 and less than 10
If the number is greater than or equal to 1, the power of 10 is positive
If the number is between 0 and 1, the power of 10 is Negative
Example: 5.34 times 10^4 equals 53,400
Example: 1.4 times 10^-1 equals 0.14
When the decimal goes to the left the exponent goes up, when the decimals goes to the right the exponent goes down.