Unit 1 real numbers

Bilingual Program MATHS UNIT 1 – REAL NUMBERS

Natural Numbers (N): The numbers used for counting. That is, the numbers 1, 2, 3, 4, etc.

Whole Numbers or Nonnegative Integers: The numbers 0, 1, 2, 3, 4, 5, etc.

Integers (Z): All positive and negative whole numbers (including zero). That is, the set: Z = {... , –3, –2, –1, 0, 1, 2, 3, ...}.

Rational Numbers (Q): All positive and negative fractions, including integers and improper fractions. Formally, rational numbers are the set of all real numbers that can be written as a ratio of integers with nonzero denominator.

Irrational Numbers (I): Real numbers that are not rational. Irrational numbers include numbers such as

,

2

29 4

,

, π, e, etc.

Real Numbers(R): All numbers on the number line. This includes (but is not limited to) positives and negatives, integers and rational numbers, square roots, cube roots , π (pi), etc.

Rounding a Number: A method of approximating a number using a nearby number at a given degree of accuracy. For example, 3.14159265... rounded to the nearest thousandth is 3.142.

That is because the third number after the decimal point is the thousandths place, and because 3.14159265... is closer to 3.142 than 3.141.

Truncating a Number: A method of approximating a decimal number by dropping all decimal places past a certain point without rounding. For example, 3.14159265... can be truncated to 3.1415. Note: If 3.14159265...were rounded to the same decimal place, the approximation would be 3.1416

Interval: The set of all real numbers between two given numbers.

The two numbers on the ends are the endpoints. The endpoints might or might not be included in the interval depending whether the interval is open, closed, or half-open (same as half-closed)  Closed Interval: An interval that contains its endpoints  Open Interval: An interval that does not contain its endpoints.  Half-Closed Interval or Half-Open Interval: An interval that contains one endpoint but not the other.

There are three main ways to show intervals: Inequalities, The Number Line and Interval

[a, b) (a, b]

Bilingual Program MATHS closed on left, open on right open on left, closed on right

a≤x<b a<x≤b

 Union and Intersection: Example: x ≤ 2 or x >3 . On the number line it would look like this:

(-∞, 2] U (3, +∞) We used a "U" to mean Union (the joining together of two sets).

There is also "Intersection" ∩, which means "has to be in both". Think "where do they overlap?".

Example: (-∞, 6] ∩ (1, ∞). The Intersection (or overlap) of those two sets goes from 1 to 6: (1, 6]

 Reading operations: o o o o

3+5=8 12 - 3 = 9 8 x 4 = 32 28 : 4 = 7

Three plus five equals eight Twelve minus seven equals nine ( Subtract 3 from 12 ) Eight times four equals thirty-two ( or eight multiplied by four equals thirty-two) Twenty-eight divided by two equals seven ( or eight divided into two equals seven)

 Reading of fractions: 1 2

17 2

= a half

3 4

= seventeen halves

= three fourths / three quarters

9 8

= nine eighths

21 = twenty-one over two hundred and sixty-five 265

 Reading of decimal numbers: o o o o o

1.827 = one point eight two seven 35.15 = thirty-five point one five 3. 1414…= three point one four repeating 3.14343….= three point one four three with four three repeating 3.01111… = Three point zero one with one repeating