Comparing Rational and Irrational Numbers

In this video, Bill Kinney discusses comparing rational and irrational numbers. He explains how to use number lines and calculators to compare rational numbers, find common denominators, and convert fractions to decimals. The video also covers techniques for comparing irrational numbers and finding numbers between them, emphasizing the importance of understanding decimal representations.

What is the main focus of Bill Kinney's video series?

• Foundations of arithmetic, algebra, and graphing

• Advanced calculus and trigonometry

• History of mathematics

• Physics and chemistry

What is the purpose of comparing numbers on a number line?

• To determine if one number is larger or smaller than another

• To solve algebraic equations

• To find the exact value of irrational numbers

• To graph complex functions

Which two rational numbers are compared in the video?

• 13/30 and 46/105

• 1/2 and 3/4

• 5/6 and 7/8

• 2/3 and 4/5

What is the first step in comparing 13/30 and 46/105?

• Estimate their values

• Convert them to percentages

• Find their square roots

• Multiply them by 100

What is the least common denominator for 13/30 and 46/105?

• 105

• 420

• 315

• 210

How can you compare rational numbers without a calculator?

• Use a graphing tool

• Estimate using fractions

• Convert to percentages

• Find a common denominator

What is the decimal representation of 13/30?

• 0.4

• 0.5

• 0.43333...

• 0.3

What is a characteristic of repeating decimals?

• They are always greater than 1

• They have no pattern

• They are irrational numbers

• They are rational numbers

How can you compare irrational numbers?

• By estimating their square roots

• By comparing their decimal representations

• By using a calculator

• By converting them to fractions

What is an example of an irrational number?

• 0.5

• Square root of 2

• 1/3

• 2/5