1.2.4 Understanding and calculating with recurring decimals

• What is the definition of recurring decimals?

  Repeating digits infinitely
• A vinculum in decimal notation covers the entire repeating sequence.

  True
• A dot above a digit in decimal notation means that only that digit repeats indefinitely.

  True
• What two symbols indicate recurring digits in decimal notation?

  Dot and line
• How is 2.141414... written as a recurring decimal?

  2.14
• The recurring decimal 0.333... is equivalent to the fraction 1/3

  True
• How is 0.232323... written as a recurring decimal?

  0.23
• What is the first step in converting recurring decimals to fractions?

  Let the decimal equal a variable
• Match the recurring decimal with its notation:

  0.444... ↔️ 0.4

  2.141414... ↔️ 2.14

  1.666... ↔️ 1.6

  0.121212... ↔️ 0.12
• Provide an example of a recurring decimal.

  0.333...
• Steps to add or subtract recurring decimals

  1️⃣ Convert recurring decimals to fractions

  2️⃣ Perform the addition or subtraction

  3️⃣ Simplify the result if needed
• Steps to multiply or divide recurring decimals

  1️⃣ Convert recurring decimals to fractions

  2️⃣ Perform the multiplication or division

  3️⃣ Simplify the result if needed
• What is the result of subtracting 0.333... from 1.666...?

  4/3
• Using fractions simplifies calculations with recurring decimals.

  True
• What is the average score of three exams where you scored 75, 80, and 85?

  80
• When four friends share 12 pizza slices equally, each friend gets 3 slices.

  True
• Steps to identify recurring decimals in decimal notation

  1️⃣ Look for a dot or a line

  2️⃣ Check if the symbol is above a repeating digit or sequence

  3️⃣ If yes, write the recurring decimal using the symbol
• If a cake is cut into 24 pieces and five students split it evenly, each student gets 4 whole pieces.

  True
• Multiplication and division of recurring decimals require the same first step as addition and subtraction.

  True
• 0.444... is a recurring decimal.

  True
• What is the result of adding 0.333... and 0.666...?

  1
• Recurring decimals have a repeating digit or sequence.

  True
• What is the result of dividing 0.666... by 0.333...?

  2
• What is the result of dividing 24 slices of cake by 5 students?

  4.8
• What is the result of subtracting the original equation from the new equation in the third step?

  9x = 3
• Recurring decimals can be directly added or subtracted without converting them to fractions.

  False