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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Describe how to check if a decimal is a rational approximation of an irrational number.
Describe one method to improve the accuracy of a rational approximation for an irrational number.
Describe the process of finding a rational approximation for an irrational number using a calculator.
Explain how you would find a rational approximation for √7.
Explain why 22/7 is considered a rational approximation of π.
Explain why irrational numbers cannot be written exactly as fractions.
Explain why rational approximations are useful in real-life calculations.
Find a rational number between 1.41 and 1.42 that can be used to approximate √2.
Which of the following fractions is closest to √5? (1) 2/1 (2) 9/4 (3) 11/5 (4) 7/3
Which of the following is a rational approximation of √10? (1) 3.16 (2) 3.14 (3) 3.18 (4) 3.12
Which of the following is a rational approximation of √12? (1) 3.46 (2) 3.45 (3) 3.47 (4) 3.44
Which of the following is a rational approximation of √17? (1) 4.12 (2) 4.10 (3) 4.15 (4) 4.20
Fill in the blank: The decimal 1.618 is a rational approximation of the ________ ratio.
Fill in the blank: The decimal 2.718 is a rational approximation of ________.
Fill in the blank: The decimal 3.14159 is a rational approximation of ________.
Fill in the blank: The fraction ________ is a common rational approximation for √2.
True or False: Every irrational number can be approximated by a rational number.
True or False: Rational approximations of irrational numbers can be made as accurate as desired.
True or False: The number √16 can be approximated by a rational number.
True or False: The number 0.101001000100001... is irrational.
