# What does "number is within 2 of a multiple of 10" mean?

I am not sure what this sentence means? It is like there is a number which is within 2 but also as a multiple of 10? Sorry, this must be incorrect. Thanks!

This probably refers to numbers compared to integer multiples of 10. Those are 10, 20, 30, 40, etc.

The number 31 is 1 away from 30, a multiple of 10. That number is within a distance of 2 from the nearest multiple of 10, so it meets the criterion.

The number 36 is 4 away from 40, the nearest multiple of 10, so it does not meet the criterion, because 4 is greater than 2.

So, subtract the number in question from the nearest multiple of 10, and compare the difference to 2. If it's greater than 2, it is not within 2 of a multiple of 10. If the difference is less than 2, it is within 2 of a multiple of 10.

Well it is clear enough what it literally means.

10 is a multiple of 10, so in that case, it means somewhere between 8 and 12, for a range of relative error of plus or minus 20%.

20 is a multiple of 10, so in that case it means somewhere between 18 and 22, for a range of relative error of plus or minus 10%.

10,000 is a multiple of 10, so in that case it means somewhere between 9998 and 10002, so in that case it means a range of error of plus or minus 0.02%.

In other words, it is a perfectly clear statement. It is also perfectly useless.

EDIT Among the mathematically aware, a "multiple" of a number almost always means an integer multiple of that number. Otherwise the phrase is utterly meaningless because every real number imaginable is a multiple of every other real number except zero.

If p and q are real numbers and q is not zero, then p/q is a real number and p is a multiple of q because (p/q) * q = p. If you do not interpret "multiple" as integer multiple, then the phrase "within 2 of a multiple of ten" simply means number.

SECOND EDIT The comments below have persuaded me to expand my answer.

The "within 2 of x" means anywhere from x minus 2 through x plus 2 inclusively. So "within 2 of 100" simply means somewhere from 98 through 102. The meaning is clear. Moreover such phrases may be of practical use. The specific one that confused you has a clear meaning; it can be defined mathematically, but it is impossible for me to see in what context outside of a classroom it would ever arise. This lack of any connection to a practical context may have contributed to your difficulty in interpreting its meaning.

• What the clause literally means can be useful, in a relevant context. One obvious relevant context would be in a programming assignment: "Write a routine to check whether a number is within 2 of a multiple of 10." Jun 2, 2020 at 5:18
• And the practical use of such a routine would be what exactly? Jun 2, 2020 at 12:57
• Passing the class, exploring alternate implementations, perhaps getting a decent golf score. Basic coding tutorials are rife with such things. Jun 2, 2020 at 13:59
• Anyway, I'm not making my point clear. Shame on me and let me start again. Pretend OP said something like "My friends live in different cities. I suggested we meet at Benihana, but they said they'd only consider places within a couple miles of somebody's home. What could that mean? Can a place be within two miles but also in several separate cities? It doesn't make sense together." I don't think a good answer would include "It is a perfectly clear statement. It is also perfectly useless." The grammar and semantics here are useful to know in everyday plain English. Jun 2, 2020 at 20:23
• OK. I agree that statements similar in structure to the one given may arise in a practical non-pegagogical setting. I shall make an edit. Jun 2, 2020 at 21:50