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3. Write three numbers whose decimal expansions are non-terminating non-recurring.

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2. Look at several examples of rational numbers in the form p/q (q ≠ 0), where p and q are integers with no common factors other than 1 and having terminating decimal representations (expansions). Can you guess what property q must satisfy?

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1. What can the maximum number of digits be in the repeating block of digits in the decimal expansion of 1/17?

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Question1: Write the following in decimal form and say what kind of decimal
expansion each has:

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Question3: Recall π is defined as the ratio of the circumference (say c) of a

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Question2: Simplify each of the following expressions:

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Question1: Classify the following numbers as rational or irrational:

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Question2: Visualise 4.26 on the number line, up to 4 decimal places.

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Question1: Visualise 3. 765 on the number line, using successive magnification.

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Question4: Classroom activity (Constructing the ‘square root spiral’): Take a large sheet of paper and construct the ‘square root spiral’ in the following fashion. Start with a point O and draw a line segment OP1 of unit length. Draw a line segment P1P2 perpendicular to OP1 of unit length. Now draw a line segment P2P3 perpendicular to OP2. Then draw a line segment P3P4 perpendicular to OP3.

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Question3: Show how √𝟓 can be represented on the number line.

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Question2: Are the square roots of all positive integers irrational? If not, give an example of the square root of a number that is a rational number.

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