Question

1) Give an example of a rational number AND an irrational number.

What is the difference between them?

2) What is the decimal equivalent of your two examples?

3) Can every repeating decimal be written as a rational number? Explain why or why
not.

Answer 1

Explanation:

A rational number is one that can be expressed as a fraction. Pi cannot be. If I tell you that the 2000th digit of pi is an 8 (which it probably isn't) and I ask you to tell me the 2001 value of pi, you have no better odds that 1/10 of getting it right.

A rational number can always be reduced to a fraction. 20 1/2 can be expressed as a fraction. It is 20.5

Pi is irrational. I don't know the value of pi beyond what a calculator can tell me. 3.14159265 The next digit is a 4. I know this only because that is what the calculator tells me.

Repeating decimals call always be represented as a fraction. For ex

x = 0.123123123123123

1000x = 123.123123123123

x = .123123123123123 Subtract

999x = 123

This comes about because in both cases what is after the decimal is the same.

x = 123/999 = 41/333