There is an old anecdote. A group of tourists visits a museum. A tourist asks the museum worker: 'How old is this statue?' The worker responds: 'It is 3005 years old.' The tourist expresses his astonishment: 'Wow, it can't be! It must be some kind of mistake!" The worker explains calmly: "At the moment I was hired, the director told me the statue is 3000 years old. I have been working here for five years already. So, 3000 + 5 = 3005."
It can be a very silly or even a shameful question for an adult, but... was the worker actually right?
I always had problems with approximate calculations. Actually, none of my teachers have ever explained it to me. I live in Moldova, and it is a poor country, although I had been studying for 18 years (lyceum, college and university). I decided to ask my question here; it's better to ask someone and to acquire some knowledge than to remain a dumbass for the rest of the life.
My first step was to assume that 3000 in this problem is an approximate number and 5 is an exact number. Then I watched a video: significant figures. It seems like in case of addition, we must keep as many decimal places as it has the addend with least number of decimal places. For example, adding 2.36 and 12.1. If those were exact numbers, the sum would be equal to 14.46. However, they're approximated numbers; 2.36 has two decimal places and 12.1 has only one. The smaller number is 1. So we must round up 14.46 to one decimal place. The result is 14.5.
Now, back to our problem. I assume 3000 has zero decimal places; 5 also has zero decimal places. 3000 + 5 = 3005. We must round up 3005 to zero decimal places and it remains as is.
So is there an error?