Question

Consider the decimal0.27227222722227...  and answer the following questions 1) is the decimal number rational or irrational? Explain. 2) assuming the pattern continues, what are the next six digits in the decimal number? 3) how many times will the digit2 appear in total before the sixth 7 in the decimal number? 4) The digit seven appears in the second decimal place, the fifth decimal place, and the ninth decimal place. what are the next three places and which the digit 7 appears? Describe the pattern.

Answer 1

Alyssan, these are the answers:

Question 1:

Let's recall that repeating decimals are considered rational numbers because they can be represented as a ratio of two integers.

Question 2:

272272

Question 3:

Three times

Question 4:

15th, 18th, 22th