INFOGRAFÍA

ACTUAL NUMBERS

6 . NUMBERS IN SCIENTIFIC NOTATION . ERROR HANDLING

5 . APPROXIMATE NUMBERS . ERRORS

4 . ROOTS AND RADICALS

2 . REAL NUMBERS

1 . IRRATIONAL NUMBERS

3 . SECTIONS OF THE ROYAL STRAIGHT

• RATIONAL

• IRRATIONAL

THE ROYAL STRAIGHT LINE

OPERATIONS WITH NUMBERS GIVEN IN SCIENTIFIC NOTATION

APPROXIMATION AND ERRORS

THE DIAGONAL OF THE SQUARE

REPRESENTACIón DE NÚMEROS SOBRE LA RECTA REAL

CONTROLLING ERROR IN A NUMBER IN SCIENTIFIC NOTATION

IRRATIONAL OTHER EXPRESSED THROUGH RADICALS

THE GOLDEN NUMBER

8 .DIRECT PROPORTIONALITY AND INVERSE PROPORTIONALITY

INVERSE PROPORTIONALITY

DIRECT PROPORTIONALITY

THE PI NUMBER

THE NUMBER e

NEPERIAN LOGARITHMS

DECIMAL LOGARITHMS

A BIT OF HISTORY

LOGARITMS WITH CALCULATOR

properties of logarithms

7 . LOGARITHMS

SEMI - STRAIGHT LINES AND REAL STRAIGHT LINES

• Numbers less than a and the proper a :

{ x / x < a }

• Numbers less than a : { x / x < a }

• Numbers greather than a : { x / x > a }

• Numbers greather than a and the proper a :

{ x / x > a }

The real line is complete , each point on the line corresponds to a real number and each real number a point on the line.

1. TWO SIMPLE LOGARITHMS

• The base is 1

2. PRODUCT & QUOTIENT

• Sum of the logarithms of the factors.
• The logarithms of a quotient is the difference between the logarithms of the dividend and the divisor.

3. POTENCY & ROOT

4. BASE CHANGE

PROPERTIES OF LOGARITHMS

Two magnitudes are directly proportional when the proportion between the two is maintained : a/b = a`/ b`with a , a`values of a magnitude and b , b`values of the other . So by increasing one, increasing the other.

SEMI - OPEN INTERVAL

• The interval [a , b) is the set of all numbers between a and b , including a but not b :

{ x / a < x < b }

• The interval (a , b] is the set of all numbers between a and b , including b but not a :

{ x / a < x < b }

Two magnitudes are inversely proportonial when : A x B = A' x B' with a , a' values of a magnitude and b , b' values of the other . So when one increases , the other decreases.

THIS IS THE FORMULA FOR THE GOLDEN NUMBER.

PROPERTIES OF POTS AND ROOTS

It is an irrational number , that is , it has infinite non - periodic decimal places.

• It´s a greek letter"p".
• The greek word perifereia means(circumference).

RATIONALIZATION OF THE DENOMINATOR

The process by which we make radicals disappear from the denominator is called denominator rationalization.

1 º case : square roots.

2 º case : other roots.

3 º case : addition and subtraction of roots.

RADICAL OPERATIONS

• SIMPLIFICATION OF RADICALS.
• RADICAL REDUCTION AT COMMON INDEX.
• EXTRACTING FACTORS OUTSIDE OF A ROOT.
• PRODUCT AND RATIO OF RADICALS OF THE SAME INDEX.
• SIMPLIFICATION OF PRODUCTS AND RADICAL RATIOS.
• POWER OF A RADICAL.
• ROOT OF A RADICAL.
• ADDITION AND SUBTRACTION OF RADICALS.

• REPRESENTATION OF FRCTIONAL NUMBERS BY THE THEOREM OF SUCH.

• REPRESENTATION OF RADICALS USING THE PYTHAGOREAN THEOREM.

• APPROXIMATE REPRESENTATION OF REAL NUMBERS.

• Significant figures : they are used to express an approximate number.

• The absolute error of an approximate measurement is the difference between the actual value and the approximate value.

Absolute error = |Real value - Approximate value|

• Relative error is the ratio of absolute error to real value. Is usually expressed in so many percent(%).

CLOSED INTERVAL

It is the set of all the numbers between a and b , both included : { x / a < x < b }

OPEN INTERVAL

It is the set of all numbers between a and b , not including a or b : {x/ a < x < b }