Ratios

Yesterday I was giving a lesson on geometric sequences to my 12^th grade students.  After explaining a very simple concept of calculating the ratio of the geometric sequence, and giving an example, we moved on to another example.

"Calculate the general term of the sequence...what information have we been given?" I asked
"The first term of the sequence!” the class yelled in unison.

“Yes, very good! What else?”

“The ratio!”

“Okay, how do we calculate the ratio?”

One of my better student raises his hand.

"We take the second term of the sequence and divide it by the first term."

"Great job! So what's the second term of the sequence?"

"2."

"And what's the first term of the sequence?"

"3."

"Okay, so what's our ratio?"

"2/3."

"Okay, awesome! Are there any questions?"

One student slowly raises his hand.
“Teacher I can't leave today without knowing one thing.”

"Okay...how can I help?"

"Teacher, I tried to calculate the ratio using my phone's calculator and 2/3 is not the answer that I'm getting."

"Okay, what answer are you getting?"

"A very long decimal."

"Are you getting 0.6666666?"

"Yes, teacher! How did you know? I am so confused..."

"Tell me this, what are you typing into your phone that gave you that decimal?"

"Teacher, I was just diving the second term by the first term in the sequence."

"No, but exactly what buttons are you pushing on your telephone?"

"Teacher, I put in those numbers that we are using."

"BUT EXACTLY WHAT NUMBERS ARE YOU PUTTING INTO YOUR PHONE? WHAT ARE YOU TYPING ON YOUR KEYPAD???"

***absolute silence for about 20 seconds***

Everyone in the entire room except this student start cracking up...including myself.  After getting everyone settled down again, I finally was able to ask, "Are you pushing 2 and then divided by and then 3?"

"Yes, teacher."

"Don't you see, that's 2/3...you don't even have to put it in the calculator!"

He didn't even get it after that.  Another classmate had to show him on a scientific calculator that 2/3 and 0.66666 are the same thing and he still had a hard time believing it.

Jfkdasl;jdkapoufioapsdfjksa;ld. Teaching in Mozambique. The struggle is real.