Rational Approximations of Irrational Numbers
Math ⇒ Number and Operations
Rational Approximations of Irrational Numbers 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 Rational Approximations of Irrational Numbers.
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
Explain how continued fractions can be used to find rational approximations of irrational numbers.
Explain how you would find a rational approximation for \( \sqrt{5} \) to two decimal places.
Explain the difference between a rational number and a rational approximation of an irrational number.
Explain why 1.414 is considered a rational approximation of \( \sqrt{2} \).
Explain why 22/7 is a better rational approximation of \( \pi \) than 3.1.
Explain why 3.14 is not exactly equal to \( \pi \), but is still useful.
A student claims that \( \frac{201}{61} \) is a better rational approximation for \( \sqrt{11} \) than \( 3.316 \). Justify whether the student is correct by calculating the decimal values and comparing their accuracy to the true value of \( \sqrt{11} \).
Given the context: A calculator gives \( \sqrt{17} \approx 4.1231056 \). Find a rational approximation in the form \( \frac{p}{q} \) that is accurate to three decimal places, and explain your reasoning.
Which of the following is a rational approximation of \( \sqrt{11} \) to two decimal places?
(1) 3.31
(2) 3.30
(3) 3.32
(4) 3.33
Which of the following is a rational approximation of \( \sqrt{19} \) to two decimal places?
(1) 4.36
(2) 4.35
(3) 4.37
(4) 4.38
Which of the following is NOT a rational approximation of \( \pi \)?
(1) 22/7
(2) 3.14
(3) 355/113
(4) 3.141592653589793238...
Which of the following is NOT an irrational number?
(1) \( \sqrt{2} \)
(2) 3.141592653...
(3) 1.5
(4) \( \sqrt{7} \)
Fill in the blank: The decimal 1.618 can be written as the fraction ________.
Fill in the blank: The decimal 1.732 can be written as the fraction ________.
Fill in the blank: The decimal 2.236 is a rational approximation of ________.
Fill in the blank: The decimal 3.162 can be written as the fraction ________.
Is 1.618 a rational approximation of the golden ratio? (Yes/No)
Is 2.236 a rational approximation of \( \sqrt{5} \)? (Yes/No)
Is 3.162 a rational approximation of \( \sqrt{10} \)? (Yes/No)
Is the number 3.1416 a rational approximation of \( \pi \)? (Yes/No)
