Comparing Irrational and Rational Numbers

This lesson teaches how to compare rational and irrational numbers. It covers comparing rational numbers by aligning decimals and using the greater than sign. It explains irrational numbers, such as those with non-repeating decimals, and how to compare them. The lesson also discusses pi, its approximation, and how to compare it with 3.14. Finally, it covers estimating square roots of non-perfect squares for more precise comparisons.

When comparing two rational numbers in decimal form, what is the first step?

• Add them together

• Multiply them by 10

• Line up the decimal points

• Convert them to fractions

How do you convert a fraction to a decimal?

• Subtract the denominator from the numerator

• Divide the numerator by the denominator

• Add the numerator and the denominator

• Multiply the numerator by the denominator

What is a key characteristic of an irrational number?

• It is a repeating decimal

• It can be expressed as a fraction

• It is a finite decimal

• It is a non-repeating, infinite decimal

Which symbol is often used to represent an irrational number that continues indefinitely?

• Question mark (?)

• Exclamation mark (!)

• Asterisk (*)

• Dot dot dot (...)

Why is pi considered an irrational number?

• It can be expressed as a fraction

• It continues indefinitely without repeating

• It is a repeating decimal

• It is exactly equal to 3.14

What is the approximate value of the square root of 7?

• Between 4 and 5

• Between 3 and 4

• Between 2 and 3

• Between 1 and 2

If 18 is closer to 16 than to 25, what can be said about the square root of 18?

• It is closer to 5 than to 4

• It is closer to 4 than to 5

• It is exactly 4.5

• It is exactly 5