Question

Xavier rounds the number "x" to the nearest integer and gets "8". Meanwhile, Yolanda rounds the same number "x" to the nearest tenth, then passes her answer to Zazeela, who rounds that answer to the nearest integer and gets 9. Yet, believe it or not, they all rounded correctly! (a) Give a specific number "x" for which this scenario could happen. Explain why it happens. (b) Describe all numbers x for which this scenario could happen.

Answer 1

(a) One possibility for x is 8.45. If you round it to an integer, you would get 8.

If you round it to the nearest tenth, you would get 8.5. Then, you round 8.5 to the nearest integer and that will give you 9.

(b) Here are the possible values for x:

8.45 ≤ x ≤ 8.49

Answer 2

a) 8.45 because rounded to the nearest integer is 8 and rounded to the nearest tenth is 8.5 which when rounded to the nearest integer is 9.
b) The numbers that fit this scenario are 8.45 to 8.49