Unit 1 Vocabulary _4º ESO_

8/3/2019 Unit 1 Vocabulary _4 ESO_

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MATH VOCABULARYUnit 1: Real number

Elvira Fuentes-Guerra Toral 4 A

M Pilar Garrido Ruiz 4 A


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SETS OF NUMBERS

NATURAL NUMBERS:

The numbers we use to count are called natural or counting numbers. Because we

begin counting with the number one, the set of natural numbers begins with numberone. The set of natural numbers is frequently denoted by N.

N = {1, 2, 3, 4, 5, , 10, 11, }

PRIME NUMBERS: its a natural number greater than one that has exactly two factors

(or divisors) itself and 1.

COMPOSITE NUMBERS: its a natural number that is divisible by a number other that

itself and 1.


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WHOLE NUMBERS: are the set of numbers that begins with number 0

INTEGER NUMBERS: The set of integersnumbers consists of the negative integers, 0,

and the positive integers. This set is frequently denoted by Z.

OPPOSITE: the opposite of a natural number, N, is N.


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ABSOLUTE VALUE of a number is its distance from 0 on a number line. The symbol or notation

for absolute value is | |. A distance is a number that is greater than or equal to 0. Since an

absolute value is a distance, the absolute value of an integer is also greater than or equal to 0

RATIONAL NUMBERS are used to express a part of a whole, a part of a quantity. Rational

numbers are the ratios of integers, also called fractions, such as = 0.5 or 1/3 = 0.333

This set is frequently denoted by Z

Fractions: A Fraction (such as 7/4) has two numbers:

Numerator

Denominator

The top number is the Numerator, it is the number ofparts you have.

The bottom number is the Denominator, it is the number ofparts the whole is divided into.

Example: 7/4 means:

-We have 7 parts

-Each part is a quarter (1/4) of a whole.


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Three Types of Fractions: There are three types of fraction:

So we can define the three types of fractions like this:

Proper Fractions: The numerator is less than the denominator

Examples:1

/3,3

/4,2

/7

Improper Fractions: The numerator is greater than (or equal to) the denominator

Examples: 4/3,11/4,

7/7

Mixed Fractions: A whole number and proper fraction together

Examples: 1 1/3, 21/4, 16

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EQUIVALENT FRACTIONS are different fractions which express the same amount.

1/2, 2/4, and 6/12 are equivalent because = 2/4 = 6/12 = 0.5

SIMPLEST FORM: When the fraction cannot be simplified, we say it is written in its

simplest form.

TERMINATING/EXACT DECIMAL is one which doesnt go on forever, so you can write

down all its digits. For example: 0.125

RECURRING DECIMAL is a decimal number which does go on forever, but where some

of the digits are repeated over and over again. For example: 0.12525252525 is arecurring decimal, where 25 are repeated forever


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IRRATIONAL NUMBER: An irrational number is a number that cannot be written as a

simple fraction. Irrational numbers are those which go on forever and dont have digits

which repeat. For example:

2 = 1. 4142135 ,

REAL NUMBER: The union of the rational numbers and the irrational numbers is the set ofreal numbers, symbolized by

INTEGER NUMBER LINE: a number line is a representation of the integer numbers in a

line.

To construct the number line, arbitrarily select a point for zero to serve as the starting point.Place the positive integers to the right of 0, equally spaced from one another. Place the

negative integers to the left of 0, using the same spacing.

PROPERTIES:The properties of the real numbers are closure, inverse, identity, associative, commutative

and distributive.


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For closure under addition, we say that for any real number x and y, (x + y) is a real

number. For multiplication, we have that for any real number x and y, (X y) is a real

number.

For the additive inverse property, we have that for any real numbers x, there exists a

real number y such that x + y = 0. The additive inverse of x is x. For the multiplicative

inverse property, we have that for any real number x, there exists a real number y such

that x y = 1. The multiplicative inverse of x is the reciprocal 1/x.

The identity property for addition states there is a real number that does not affect theany other real number when it is added to it, namely 0. For multiplication, we have a


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real number that does not affect any other real number when it is multiplied by it; that

number is 1.

The associative property tells us that if we add or multiply three real numbers together

with two operations, it does not matter which of the two operations we do first.

The commutative property tells us that if we are adding or multiplying two real

numbers, we can flip the sides of the operands and we will get the same result.

The distributive property tells us that a real number that is multiplied by a sum of two

real numbers is equal to the sum of the first number times the sum of each of the real

numbers in the sum.

INTERVAL: A set is a collection of unique elements. Elements in a set do not repeat.

Sets may be described in many ways: by set-builder notation, by interval notation or by

graphing on a number line.


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Set-builder notation:

Interval notation:

Graphs or diagrams:


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ROUNDING:

Rounding a number is another way of writing a number approximately. There are several

different methods for rounding.

-Leave it the same if the next digit is less than 5 (this is called rounding down)

-But increase it by 1 if the next digit is 5 or more (this is called rounding up)

ESTIMATION AND APROXIMATION:

Estimation and approximation are important elements of the non-calculator examination

paper. You will be required to give estimation by rounding numbers to convenient

approximations, usually one significant figure.

ABSOLUTE ERROR: is the difference between the Exact Value and the approximate value.Sometimes is impossible to know the exact value of a number, then the Absolute Value

depends on the approximation.


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Absolute error = I Exact Value Approximate value I

RELATIVE ERROR:is the absolute error divided by the magnitude of the exact value. The

percent error is the relative error expressed in terms of per 100.We need to know the

value or the percentage of the relative error to determine the accuracy of differentmeasurements or approximations. So it is a comparative tool.

Unit 1 Vocabulary _4º ESO_

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