Real Number System

Math ⇒ Number and Operations

Real Number System starts at 8 and continues till grade 12. QuestionsToday has an evolving set of questions to continuously challenge students so that their knowledge grows in Real Number System. How you perform is determined by your score and the time you take. When you play a quiz, your answers are evaluated in concept instead of actual words and definitions used.

See sample questions for grade 10

Express 0.16 (where 6 is repeating) as a fraction in simplest form.

Express 0.6 (where 6 is repeating) as a fraction in simplest form.

Express 0.777... as a fraction in simplest form.

Express 3.25 as a fraction in simplest form.

If a number can be written as a/b, where a and b are integers and b ≠ 0, what type of number is it?

If x = √5 and y = 2, what is x + y? Is the result rational or irrational?

If x = 2/7, write x as a decimal up to 4 decimal places.

Is the number 0.123456789101112... (where the digits are written in order) rational or irrational?

Is the number 1.01001000100001... (where the number of zeros between ones increases by one each time) rational or irrational?

Is the number π rational or irrational?

Write the decimal expansion of 1/8.

Write the number √49 as a rational number.

Consider the number √50. Express it in the form a√b, where a and b are integers and b is square-free. Is the result rational or irrational?

If x = √2 and y = √8, express x × y in simplest form and state whether the result is rational or irrational.

If x = 0.232332333233332..., where the number of 3's between each 2 increases by one each time, is x rational or irrational?

If x is a nonzero rational number and y is an irrational number, is x/y always irrational? Answer Yes or No and justify your answer.

Let a = 2 + √3 and b = 2 - √3. Calculate a × b and state whether the result is rational or irrational.

Prove that the sum of a rational number and an irrational number is always irrational.