If you take the context away: When you learn that in school, it’s pointed out as a mistake if you write 10 000m. You should have converted that into 10km to get a perfect score.
But there are certainly contexts where it makes sense to stay with one prefix. For example if you write things into a table. Or when your number is basis for a calculation that surely ends you up in the next bigger or smaller realm of numbers.
I’m not sure if it’s necessarily the case for comparing stuff… It’s kind of rare that you have things that are a factor of 10000 or a million apart, so it’s kind of difficult for me to find examples. But I have capacitors that are 470uF or 22pF and resistors that are 220 Ohm or a Mega-Ohm or 150kOhm. They’re all wired into one circuit.
I know how to handle that and switch between all of them. So people do switch and that’s kind of the point of having those prefixes. If I type things like that into my calculator, I use scientific notation and after the calculation I use the special key to find me the closest power of ten. I forgot the name of that key. ‘E’ or ‘ENG’. It makes it very easy, you just type in 470e-6 or 22e-9 and it figures it out for you, no matter how convoluted. You need to remember your powers of ten, but you already do that for at least half of them. I think most people know how many zeros are in a million or a thousand.
On the other hand, if i say I’m dividing the road into sections of 100m, im not going to say I’m dividing 2km into 100m sections, but 2000m.
The ‘offerings’ example is good. Because for example internet providers are all over the place. I’ve had a 16000 dsl line, 16Mbit is the same, and nowadays there is anything between 50 to 1000Mbit/s and some advertise it as 1000Mbit, some as a Gigabit line. But they want to sell stuff, not do maths correctly…
If you take the context away: When you learn that in school, it’s pointed out as a mistake if you write 10 000m. You should have converted that into 10km to get a perfect score.
Only if this was explicitly demanded. If the teacher doesn’t, and then claim 10000m is “wrong”, the teacher is wrong.
I think I had a strict maths teacher. But they told us upfront how to convert units and how to do the rounding. So there were no ambiguities.
But I’ve also come to the conclusion that humans can handle numbers up to the ten or hundred thousands as well. We mostly do that instead of converting past kilo. And even textbooks say the sun is on average 150 million kilometers away.
Hmm, halfway…
If you take the context away: When you learn that in school, it’s pointed out as a mistake if you write 10 000m. You should have converted that into 10km to get a perfect score.
But there are certainly contexts where it makes sense to stay with one prefix. For example if you write things into a table. Or when your number is basis for a calculation that surely ends you up in the next bigger or smaller realm of numbers.
I’m not sure if it’s necessarily the case for comparing stuff… It’s kind of rare that you have things that are a factor of 10000 or a million apart, so it’s kind of difficult for me to find examples. But I have capacitors that are 470uF or 22pF and resistors that are 220 Ohm or a Mega-Ohm or 150kOhm. They’re all wired into one circuit. I know how to handle that and switch between all of them. So people do switch and that’s kind of the point of having those prefixes. If I type things like that into my calculator, I use scientific notation and after the calculation I use the special key to find me the closest power of ten. I forgot the name of that key. ‘E’ or ‘ENG’. It makes it very easy, you just type in 470e-6 or 22e-9 and it figures it out for you, no matter how convoluted. You need to remember your powers of ten, but you already do that for at least half of them. I think most people know how many zeros are in a million or a thousand.
On the other hand, if i say I’m dividing the road into sections of 100m, im not going to say I’m dividing 2km into 100m sections, but 2000m.
The ‘offerings’ example is good. Because for example internet providers are all over the place. I’ve had a 16000 dsl line, 16Mbit is the same, and nowadays there is anything between 50 to 1000Mbit/s and some advertise it as 1000Mbit, some as a Gigabit line. But they want to sell stuff, not do maths correctly…
Only if this was explicitly demanded. If the teacher doesn’t, and then claim 10000m is “wrong”, the teacher is wrong.
I think I had a strict maths teacher. But they told us upfront how to convert units and how to do the rounding. So there were no ambiguities.
But I’ve also come to the conclusion that humans can handle numbers up to the ten or hundred thousands as well. We mostly do that instead of converting past kilo. And even textbooks say the sun is on average 150 million kilometers away.