Irrational NumbersUnit 1.07

VocabularyRational Number: A Rational Number is a number that CAN be written as a fraction.

Example: Which of the following are rational numbers? (Write the rational numbers in the circle and those that are not rational in the circle)A) B) C)

D) E) F)π

VocabularyIrrational Number: An Irrational Number is a number that CANNOT be written as a fraction.

Example: Which of the following are irrational numbers? (Write the irrational numbers in the circle and those that are not irrational in the circle)A) B) C)

D) E) F)

π

If it’s NOT Rational…

Then it IS… ? Irrational!

Rational or Irrational?

Finger Flip! ⅗

Rational or Irrational?

Finger Flip!

Rational or Irrational?

Finger Flip!

Rational or Irrational?

Finger Flip!

Rational or Irrational?

Finger Flip!

Rational or Irrational?

Finger Flip!

Rational or Irrational?

Finger Flip!

Rational or Irrational?

Finger Flip!

Rational or Irrational?

Finger Flip! π

Rational or Irrational?

Finger Flip!

Rational or Irrational?

Finger Flip!

HOW DO YOU WRITE A REPEATING DECIMAL

AS A FRACTION?

How do I … ?Writing a rational number as a fraction: You can write any rational number (with repeating digits) as a fraction by following these 4 steps.

Step 1: Set the given number equal to n.

Step 2: Multiply both sides by the power of 10 that equals the number of repeating digits.

Step 3: Subtract & Divide.

Step 4: Reduce (if possible).

Example #1:Write the rational number as a fraction.

Step 1: Set the given number equal to n.

Step 2: Multiply both sides by the power of 10 that equals the number of repeating decimals.

Step 3: Subtract & Divide.Step 4: Reduce (if possible).

Example #2:Write the rational number as a fraction.

Step 1: Set the given number equal to n.

Step 2: Multiply both sides by the power of 10 that equals the number of repeating decimals.

Step 3: Subtract & Divide.Step 4: Reduce (if possible).

Let’s Practice! #1Write the rational number as a fraction.

Step 1: Set the given number equal to n.

Step 2: Multiply both sides by the power of 10 that equals the number of repeating decimals.

Step 3: Subtract & Divide.Step 4: Reduce (if possible).

Write the rational number as a fraction.

Step 1: Set the given number equal to n.

Step 2: Multiply both sides by the power of 10 that equals the number of repeating decimals.

Step 3: Subtract & Divide.Step 4: Reduce (if possible).

Let’s Practice! #2

Write the rational number as a fraction.

Step 1: Set the given number equal to n.

Step 2: Multiply both sides by the power of 10 that equals the number of repeating decimals.

Step 3: Subtract & Divide.Step 4: Reduce (if possible).

Let’s Practice! #3

Write the rational number as a fraction.

Step 1: Set the given number equal to n.

Step 2: Multiply both sides by the power of 10 that equals the number of repeating decimals.

Step 3: Subtract & Divide.Step 4: Reduce (if possible).

Let’s Practice! #4

Write the rational number as a fraction.

Step 1: Set the given number equal to n.

Step 2: Multiply both sides by the power of 10 that equals the number of repeating decimals.

Step 3: Subtract & Divide.Step 4: Reduce (if possible).

Let’s Practice! #5

HOMEWORK TIME! Is This Rational? WS

WHAT IF THERE ARE NON-REPEATING

DIGITS?1.07 day 2

How do I … ?Writing a rational number as a fraction when not all digits are repeating: You can write any rational number (with repeating & non-repeating digits) as a fraction by following these 6 steps.

Step 1: Move the decimal point behind the last repeating digit.Step 2: Multiply by the power of 10 that equals the number of

places you moved the decimal point.Step 3: Move the decimal point in front of the 1st repeating digit.Step 4: Multiply by the power of 10 that equals the number of

places you moved the decimal point.Step 5: Subtract & Divide.Step 6: Reduce (if possible).

Example #3:Write the rational number as a fraction.

Step 1: Move the decimal point behind the last repeating digit.

Step 2: Multiply by the power of 10 that equals the number of places you moved the decimal point.

Step 3: Move the decimal point in front of the 1st repeating digit.

Step 4: Multiply by the power of 10 that equals the number of places you moved the decimal point.

Step 5: Subtract & Divide.Step 6: Reduce (if possible).

Example #4:Write the rational number as a fraction.

Step 1: Move the decimal point behind the last repeating digit.

Step 2: Multiply by the power of 10 that equals the number of places you moved the decimal point.

Step 3: Move the decimal point in front of the 1st repeating digit.

Step 4: Multiply by the power of 10 that equals the number of places you moved the decimal point.

Step 5: Subtract & Divide.Step 6: Reduce (if possible).

Write the rational number as a fraction.

Let’s Practice! #6Step 1: Move the decimal point behind

the last repeating digit.Step 2: Multiply by the power of 10 that

equals the number of places you moved the decimal point.

Step 3: Move the decimal point in front of the 1st repeating digit.

Step 4: Multiply by the power of 10 that equals the number of places you moved the decimal point.

Step 5: Subtract & Divide.Step 6: Reduce (if possible).

Write the rational number as a fraction.

Let’s Practice! #7Step 1: Move the decimal point behind

the last repeating digit.Step 2: Multiply by the power of 10 that

equals the number of places you moved the decimal point.

Step 3: Move the decimal point in front of the 1st repeating digit.

Step 4: Multiply by the power of 10 that equals the number of places you moved the decimal point.

Step 5: Subtract & Divide.Step 6: Reduce (if possible).

Write the rational number as a fraction.

Let’s Practice! #8Step 1: Move the decimal point behind

the last repeating digit.Step 2: Multiply by the power of 10 that

equals the number of places you moved the decimal point.

Step 3: Move the decimal point in front of the 1st repeating digit.

Step 4: Multiply by the power of 10 that equals the number of places you moved the decimal point.

Step 5: Subtract & Divide.Step 6: Reduce (if possible).

Write the rational number as a fraction.

Let’s Practice! #9Step 1: Move the decimal point behind

the last repeating digit.Step 2: Multiply by the power of 10 that

equals the number of places you moved the decimal point.

Step 3: Move the decimal point in front of the 1st repeating digit.

Step 4: Multiply by the power of 10 that equals the number of places you moved the decimal point.

Step 5: Subtract & Divide.Step 6: Reduce (if possible).

HOMEWORK TIME! Rational Conversion! WS