Exploring Real Numbers. About Real Numbers ● "Real Numbers" are all the numbers that we deal with in math class and in life! ● Real Numbers can be thought.

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Presentation transcript:

Exploring Real Numbers

About Real Numbers ● "Real Numbers" are all the numbers that we deal with in math class and in life! ● Real Numbers can be thought of as all the points that fall along a number line.

Real Numbers (R) all numbers that are points on a number line

Let's be rational...or irrational! ● Real numbers can be divided into two categories: REAL NUMBERS Irrational Rational

Rational Numbers ( ℚ ) ● any number that can be written as a fraction 1/ /3 -1/3 ● any decimal that terminates (ends) or repeats

Rational Numbers (Q) any number that can be written as a fraction (includes terminating and repeating decimals) Real Numbers (R) all numbers that are points on a number line

Irrational Numbers ( I )* ● any number that can not be written as a fraction (as a ratio of 2 whole numbers) ● a non-repeating, non-terminating decimal

Rational Numbers (Q) any number that can be written as a fraction (includes terminating and repeating decimals) Irrational Numbers (I*) any number that cannot be written as a fraction. Non- terminating, non- repeating decimals Real Numbers (R) all numbers that are points on a number line

Rational Number Breakdown ● Rational numbers can be divided into 3 categories REAL NUMBERS RationalIrrational Natural Numbers Whole Numbers Integers

Natural Numbers ( ℕ ) ● Natural numbers are the counting numbers. They are probably the first numbers you learned about. 1, 2, 3, 4, 5...

Rational Numbers (Q) any number that can be written as a fraction (includes terminating and repeating decimals) Natural Numbers (N) counting numbers Irrational Numbers (I*) any number that cannot be written as a fraction. Non- terminating, non- repeating decimals Real Numbers (R) all numbers that are points on a number line

Whole Numbers ( W ) ● Add a zero to the Natural Numbers and you'll get the set called "Whole Numbers" 0, 1, 2, 3, 4, 5...

Rational Numbers (Q) any number that can be written as a fraction (includes terminating and repeating decimals) Whole Numbers (W) counting numbers and zero Natural Numbers (N) counting numbers Irrational Numbers (I*) any number that cannot be written as a fraction. Non- terminating, non- repeating decimals Real Numbers (R) all numbers that are points on a number line

Integers ( ℤ ) ● Integers include all counting numbers, their opposites, and zero ● The opposites of the counting numbers are simply the negatives... -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5...

Rational Numbers (Q) any number that can be written as a fraction (includes terminating and repeating decimals) Integers (Z) whole numbers and their opposites Whole Numbers (W) counting numbers and zero Natural Numbers (N) counting numbers Irrational Numbers (I*) any number that cannot be written as a fraction. Non- terminating, non- repeating decimals Real Numbers (R) all numbers that are points on a number line

Rational Numbers (Q) any number that can be written as a fraction (includes terminating and repeating decimals) Integers (Z) whole numbers and their opposites Whole Numbers (W) counting numbers and zero Natural Numbers (N) counting numbers Irrational Numbers (I*) any number that cannot be written as a fraction. Non- terminating, non- repeating decimals Real Numbers (R) all numbers that are points on a number line

Pop Quiz! ● Name the set(s) of numbers to which each number belongs

Pop Quiz! ● Name the set(s) of numbers to which each number belongs  (integers, rational numbers)

Pop Quiz! ● Name the set(s) of numbers to which each number belongs  (integers, rational numbers)

Pop Quiz! ● Name the set(s) of numbers to which each number belongs  (integers, rational numbers)  (rational numbers)

Pop Quiz! ● Name the set(s) of numbers to which each number belongs  (integers, rational numbers)  (rational numbers) /4

Pop Quiz! ● Name the set(s) of numbers to which each number belongs  (integers, rational numbers)  (rational numbers) /4  (integers, rational numbers)

Pop Quiz! ● Name the set(s) of numbers to which each number belongs  (integers, rational numbers)  (rational numbers) /4  (integers, rational numbers) 4. 7

Pop Quiz! ● Name the set(s) of numbers to which each number belongs  (integers, rational numbers)  (rational numbers) /4  (integers, rational numbers) 4. 7  (natural numbers, whole numbers, integers, rational numbers)

Exploring Real Numbers THE END