Question about page 280: Chapter 4.8, Exercises 2&4

[MetallicCrimson]

Alright, alright, but what if the real result goes haywire in the digits that have been cut off? For example

40.7272727272748946811896434...

On the other hand, arriving at such a number could be problematic with a 13-digit calculator. It's most likely a repeating pattern of 40.7272..., but can we be sure about it?

(Kind of) similarly, in ex. 4:

It might not be true if the calculator rounds the answer. For example, here's a screenshot of one of my favourite tools, Desmos:

(This isn't a suggestion or anything, I was just curious what you think.)

[spamegg1]

Well those are good points; I'll mention them and for the solution I'll add the assumption that it's repeating forever.

I think the author implied that it is assumed to be repeating, from how the text is written. I looked through the book but there are no statements on the assumptions of how a calculator works. Obviously she's a classroom teacher and the book is intended to be used in a classroom; American students are often required to buy these calculators. So "how a calculator works assumptions" are supposed to be obvious to the students from direct usage.

[MetallicCrimson]

Sounds reasonable. I just thought it was intended to be a trick question, which would make assuming anything from the way calculators work false, but mentioning these points is perfectly fine.
Thanks!

[spamegg1]

The example with 0.20000000000000001 being "rounded" to 0.2 might be just correcting a typical floating point inaccuracy. So that might be intended and correct.

I'm not sure how "classroom calculators" differ in their functionality from "programming language calculators". Programming languages have to use IEE 754 standard generally but maybe physical calculators don't do that.

With classroom calculators the assumption might be: "if you don't see repeating patterns then it's rational". Assuming the calculator has more than 2 digits to display 😆 then 0.2 would be assumed rational.

Anyway I'll just write up something. 😆