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Recurring Decimals Introduction

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Recurring Decimals Introduction worksheet preview

Recurring Decimals Introduction

Recurring decimal pattern illustration

📚 Part 1: Understanding Recurring Decimals

1. Which of these decimals are recurring? Circle your answers.

0.25

0.333...

0.75

0.272727...

2. What does the notation 0.3̄ mean?

The decimal stops at 0.3

The 3 repeats forever

The decimal equals 3

The 3 appears three times

3. Which fractions will produce terminating decimals? Tick all that apply.

1/4

1/3

3/8

2/9

4. Write these recurring decimals using dot notation:

a) 0.666... = 0.______

b) 0.181818... = 0.______

c) 0.142857142857... = 0.______

✏️ Part 2: Converting Fractions to Decimals

5. Use long division to convert these fractions to decimals. Show your working.

a) 1/3 = ______

b) 2/11 = ______

c) 5/6 = ______

6. Complete this table by converting each fraction to a decimal and stating whether it terminates or recurs:

Fraction | Decimal | Terminating or Recurring?

1/8 = ______ | ______

1/7 = ______ | ______

3/5 = ______ | ______

4/9 = ______ | ______

7. Explain why 1/4 gives a terminating decimal but 1/3 gives a recurring decimal.

🧠 Part 3: Problem Solving

8. A calculator shows 0.16666667 when you divide 1 by 6. What is the actual recurring decimal?

Answer: ______

9. Which fraction equals 0.090909...? Show your reasoning.
10. Challenge: If x = 0.727272..., find the value of x as a fraction.

Hint: Try multiplying x by 100 and see what happens!

x = ______

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