Number Systems quiz

Which of these is an irrational number?

The decimal expansion of 1/8 is:

0.3333... in the form p/q is:

The value of 27^(1/3) is:

Every point on the number line represents a:

The product of sqrt(3) and sqrt(12) is:

Between two rational numbers there are:

The decimal expansion of an irrational number is:

The value of 9^(-1/2) is:

Rationalising 1/sqrt(2) gives:

Is zero a rational number? Write it in the form p/q. (2 marks)

Find two rational numbers between 1/2 and 3/4. (2 marks)

Write the decimal expansion of 10/3 and state its type. (2 marks)

Without dividing, decide whether 13/40 has a terminating decimal expansion. Give a reason. (2 marks)

Simplify 2^(2/3) x 2^(1/3). (2 marks)

Simplify (sqrt(5) + sqrt(3))(sqrt(5) - sqrt(3)). (2 marks)

Give an example of two irrational numbers whose product is rational. (2 marks)

State whether true or false with a reason: every integer is a rational number. (2 marks)

Find the value of (125)^(2/3). (2 marks)

Express 0.18181818... in the form p/q. (2 marks)

Express 2.353535... and 0.2353535... in the form p/q. (3 marks)

Rationalise and simplify 6/(3 - sqrt(3)). (3 marks)

Simplify: (i) 11^(1/2)/11^(1/4) (ii) 7^(1/2) x 8^(1/2) (iii) (3^(1/2))^4. (3 marks)

If x = 3 + 2 sqrt(2), find 1/x and x + 1/x. (3 marks)

Find the value of (sqrt(3) + sqrt(2))^2 + (sqrt(3) - sqrt(2))^2. (3 marks)

Read the passage and answer the questions. A square garden has an area of 2 square m. Riya wants to fence it and needs the length of one side. (i) Find the side of the garden. (ii) Is this length rational or irrational? (iii) Show how to locate this length on the number line. (5 marks)

Read the passage and answer the questions. A student divides 22 by 7 and gets 3.142857142857..., and says this is the exact value of pi. (i) Is 22/7 rational or irrational? (ii) Is pi rational or irrational? (iii) Why is the student's claim wrong? (5 marks)

Read the passage and answer the questions. A shopkeeper's calculator shows the price per gram of a spice as 0.454545... rupees. (i) What type of decimal expansion is this? (ii) Convert it to the form p/q. (iii) What is the cost of 22 grams at this rate? (5 marks)

Read the passage and answer the questions. In a science experiment, a quantity is written as 8^(2/3) units and another as 16^(-1/4) units. (i) Find the value of 8^(2/3). (ii) Find the value of 16^(-1/4). (iii) Find their product. (5 marks)

Read the passage and answer the questions. A carpenter cuts a right-angled triangular piece with legs 1 m and 2 m. (i) Find the length of the hypotenuse. (ii) Is it rational or irrational? (iii) Rationalise 1 divided by this length. (5 marks)

Explain the classification of real numbers using a flowchart showing natural, whole, integer, rational and irrational numbers, with two examples of each. (6 marks)

Construct the square root spiral up to sqrt(5) and explain each step. (6 marks)

Show how to represent sqrt(9.3) on the number line geometrically. Explain the construction and why it works. (6 marks)

Rationalise the denominators and simplify: (i) (3 + sqrt(2))/(3 - sqrt(2)) (ii) (sqrt(5) - sqrt(3))/(sqrt(5) + sqrt(3)). (6 marks)

Use successive magnification on the number line to visualise 4.26 recurring up to four decimal places. Explain why every real number has a unique position on the number line. (6 marks)