Approximating Irrational Numbers and Decimals

This lesson teaches how to approximate the value of irrational numbers. It begins by explaining the difference between rational and irrational numbers, focusing on the types of decimals associated with each. The lesson then provides a method for approximating the value of irrational numbers, using the square root of 5 as an example. By finding the two perfect squares between which an irrational number falls, students can estimate its value. The lesson concludes with a summary of the approximation method.

What is the main goal of this lesson?

• To approximate the value of irrational numbers.

• To memorize the values of common irrational numbers.

• To learn how to calculate the exact value of irrational numbers.

• To understand the difference between rational and irrational numbers.

Which of the following is a characteristic of a rational number?

• It is always a whole number.

• It always has a non-repeating decimal.

• It cannot be expressed as a fraction.

• It can be written as a fraction of two integers.

What type of decimal is 4.56?

• Irrational decimal

• Non-terminating decimal

• Terminating decimal

• Repeating decimal

Which of the following is an example of a repeating decimal?

• 5.123456

• 4.56

• 2.333...

• 3.14159

What defines an irrational number?

• It has a repeating decimal pattern.

• It can be expressed as a fraction.

• It cannot be written as a fraction and has a non-repeating decimal.

• It is always a whole number.

Which of the following is an example of an irrational number?

• 3.14

• 1/2

• Square root of 2

• 0.333...

What is the first step in approximating the value of an irrational number?

• Convert the number into a fraction.

• Round the number to the nearest whole number.

• Identify two perfect squares between which the number lies.

• Find the exact value using a calculator.

Which perfect squares are used to approximate the square root of 5?

• 1 and 4

• 4 and 9

• 9 and 16

• 16 and 25

How do you determine which perfect square the square root of 5 is closer to?

• By using a calculator to find the decimal value.

• By comparing the distances to the perfect squares.

• By calculating the exact value of the square root of 5.

• By guessing based on intuition.

What is the approximate value of the square root of 5 using the method described?

• 3.0

• 2.0

• 2.2

• 2.5