warm-up. real numbers the real numbers flow chart real numbers rational irrational integers whole...

WARM-UP

REAL NUMBERS

THE REAL NUMBERS FLOW CHARTREAL NUMBERS

RATIONAL IRRATIONAL

INTEGERS

WHOLE

NATURAL

Real Numbers: numbers found on the number line; both rational and irrational.

Rational Numbers: numbers that can be written as fractions. What about decimals?

Irrational Numbers: numbers that cannot be written as fractions.What about decimals?

Integers: whole numbers and their opposites. {...-3, -2, -1, 0, 1, 2, 3,...}

Whole Numbers: a nonnegative integer. What about fractions? Decimals? Zero?

Natural Numbers: the counting numbers. {1, 2, 3, 4,...}

Rational

Irrational

Integer Whole Natural

.23

-7

1.9876…½

19

0

Classify the following numbers

PERFECT SQUARES AND SQUARE ROOTS

• PERFECT SQUARE- A NUMBER MADE BY SQUARING A WHOLE NUMBER• WHAT DOES THIS MEAN?

• LIST THE PERFECT SQUARES 1-20 AND 25

• THE SQUARE ROOT OF AN NUMBER IS A VALUE THAT, WHEN MULTIPLIED BY ITSELF, GIVES THE NUMBER.

SQUARE ROOTS

• •

WARM-UP: IDENTIFY EVERY CATEGORY THAT EACH REAL NUMBER FITS IN.Rational

Irrational

Integer

Whole Natural

3.23

-9

2.987…¾

21

0

IRRATIONAL NUMBERS

• A NUMBER THAT CANNOT BE WRITTEN AS FRACTION OR REPEATING/TERMINATING DECIMAL

• THE MOST FAMOUS IRRATIONAL NUMBER: • NON-PERFECT SQUARES• WHAT WOULD AN EXAMPLE OF A NON-PERFECT SQUARE?

RATIONAL VS. IRRATIONAL

ESTIMATING SQUARE ROOTS

• WE CAN USE PERFECT SQUARES TO HELP US APPROXIMATE THE VALUE OF ANY NON-PERFECT SQUARE. WHEN TAKING THE SQUARE ROOT OF A NUMBER THAT IS NOT A PERFECT SQUARE, USE THE TWO SURROUNDING PERFECT SQUARES TO ASSIST IN ESTIMATING THE SQUARE ROOT.

• EXAMPLES

1.

2.

3. FIND THE SUM OF ALL OF THE INTEGERS BETWEEN AND

ORDER NUMBERS FROM LEAST AND GREATEST

EXIT TICKET

• ESTIMATE TO THE NEAREST TENTH

• PLACE THE FOLLOWING NUMBERS IN ORDER

-4, 3.16, -1.25, ,