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 10
Calculate the value of 22/7 to two decimal places.
Calculate the value of 355/113 to three decimal places.
Calculate the value of 7/5 to two decimal places.
Calculate the value of 99/70 to three decimal places.
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.
Explain why every rational approximation of an irrational number is only an estimate.
Explain why rational approximations are useful when working with irrational numbers.
Find a rational approximation of \sqrt{13} to two decimal places.
Find a rational approximation of \sqrt{23} to two decimal places.
Find a rational approximation of \sqrt{7} to two decimal places.
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} .
Explain why the decimal expansion of a rational approximation of an irrational number must eventually terminate or repeat, while the decimal expansion of the irrational number itself does not.
Given that \sqrt{2} \approx 1.41421356 , find a rational number in the form \frac{p}{q} such that its decimal value is accurate to four decimal places of \sqrt{2} . Show your calculation.
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.
