Rational Approximations of Irrational Numbers
Math ⇒ Number and Operations
Rational Approximations of Irrational Numbers starts at 8 and continues till grade 12.
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See sample questions for grade 9
Explain how to check if a decimal is a rational approximation of an irrational number.
Explain how you would find a rational approximation for \( \sqrt{11} \).
Explain the difference between a rational number and a rational approximation.
Explain why \( \sqrt{2} \) cannot be written as a fraction.
Explain why rational approximations are useful when working with irrational numbers.
If \( \sqrt{17} \approx 4.123 \), what is its value rounded to one decimal place?
If \( \sqrt{18} \approx 4.243 \), what is its value rounded to one decimal place?
If \( \sqrt{6} \approx 2.449 \), what is its value rounded to two decimal places?
Which of the following fractions is closest to \( \pi \)?
(1) \( \frac{22}{7} \)
(2) \( \frac{3}{2} \)
(3) \( \frac{7}{5} \)
(4) \( \frac{5}{2} \)
Which of the following is a rational approximation of \( \sqrt{21} \)?
(1) 4.58
(2) 4.50
(3) 4.00
(4) 5.00
Which of the following is a rational approximation of \( \sqrt{8} \)?
(1) 2.83
(2) 2.50
(3) 2.00
(4) 3.00
Which of the following is NOT a rational approximation of \( \sqrt{12} \)?
(1) 3.46
(2) 3.50
(3) 3.00
(4) 3.46
Fill in the blank: The decimal 1.414 is a rational approximation of ________.
Fill in the blank: The decimal 1.618 is a rational approximation of the ________ ratio.
Fill in the blank: The decimal 1.732 is a rational approximation of ________.
Fill in the blank: The decimal 2.236 is a rational approximation of ________.
Is 1.732 a rational approximation of \( \sqrt{3} \)? (Yes/No)
Is 1.732 a rational number? (Yes/No)
Is 2.236 a rational number? (Yes/No)
Is 3.142 a rational approximation of \( \pi \)? (Yes/No)
