Lesson 1.1 - Rational & Irrational Numbers Rational Numbers are any number that can be written as a fraction and simplified into either a Whole Number, a Repeating Decimal or a Terminating Decimal.
Irrational Numbers are numbers that do NOT fall into any of these categories.
To write a fractions as a decimal you first need to know that a FRACTION means to DIVIDE, so the TOP number goes INTO the division box and the BOTTOM number goes OUTSIDE. Add a decimal to begin annexing zeros and keep going until it either stops (terminating decimal) or repeats (repeating decimal).
To write a decimal as a fraction you need to know your PLACE VALUES, so if a decimal has 2 digits in it you have to write it as a fraction over 100 (2 digits represents 2 zeros in 100!) and if a decimal has 3 digits in it you have to put it over 1,000! If a decimal is REAPEATING using BAR NOTATION you don't put it over 10, 100 or 1,000...you go down to 9, 99 or 999! So 0.3 repeating would be written as 3/9
Square Roots means find a number that when times itself equals that number: The SqRt of 81 = 9 because 9 x 9 = 81
Cube Root means find a number that multiplies 3 times to equal something else: The CbRt of 27 = 3 because 3 x 3 x 3 = 27
To estimate Square Roots (yes...we can't use a calculator for this...sorry!) you have to find the nearest Square Root bigger and smaller than the number so the SqRt of 11 would be SqRt 9 and SqRt 16 because they are the two closest. Now your answer is between 3 and 4 (those are the answers) so you can say 3.4 is an estimate but if I wanted you to go even smaller or more exact, you have to try squaring 3.4 (11.56) and 3.3 (10.89) to see where the number 11 would fall! This means that the BEST answer is 3.35 because it is between 3.3 and 3.4 (write it as 3.30 and 3.40 to see why 3.35 is the middle!!!)
Lesson 1.2 Classifying Real Numbers ALL numbers are considered REAL! but then there are 2 sub categories...Rational and Irrational Rational numbers are fractions and decimals that repeat or terminate and can be positive or negative The next category are Integers; these are WHOLE numbers only but NEGATIVES!!! The final category are Whole Numbers; these are the same as integers but POSITIVES only!!! REAL - RATIONAL - INTEGER - WHOLE Irrational numbers are their own category and don't have any sub categories. REAL - IRRATIONAL