# Thread: Difference? "Smallest nonzero 4-digit number", "Smallest 4 nonzero digit number"

1. ## Difference? "Smallest nonzero 4-digit number", "Smallest 4 nonzero digit number"

Hi, My child is studying in grade 5. I am not able to make him understand the difference between the following 2 questions:
1) What is smallest non zero four digit number

2) What is smallest four non zero digit number

The answer to the above questions are different. Can anyone please explain the difference between the two?

2. ## Re: non zero

I'm going to assume we CANNOT use negative numbers. It might be a bit different if negative numbers are allowed.

Originally Posted by romy
1) non zero four digit number
These must have four digits, but due to convention, leading zeros don't count. The FIRST digit must not be zero.
Four-digit numbers are restricted to this range: 1000 through 9999. This makes it a little silly to require that it be "nonzero". We call this sort of silliness "redundant".

Examples: 1000, 2945, 3030
NONExample: 0002 <== Silly, since no one writes '2' in this way.

2) four non zero digit number
This is a little more restrictive for four digit numbers, but really does not restrict us to four digit numbers. It requires that NONE of the digits is zero in a four-digit number. Clearly, the first digit already wasn't.[/quote]

Examples: 1111, 2345, 9182, 92930, 78034, 746007
NONExample: 1110 <== Whoops. Only three nonzero digits.
NONExample: 2300 <== Whoops. Only two nonzero digits.
NONExample: 740007 <== Whoops. Only three nonzero digits.
Possible Example: 21212 <== While this has five nonzero digits, it certainly also has four nonzero digits. The problem statement did NOT say ONLY four.

Well, that was fun.

3. ## non zero

thank you for your simple answer, but does it mean that 32450 also can be considered a four non zero digit?

4. Originally Posted by Rehab Waked
thank you for your simple answer, but does it mean that 32450 also can be considered a four non zero digit?
If one assumes "four nonzero-digit number" to mean "any number which contains at least four nonzero digits", then "yes".

If one assumes "four nonzero-digit number" to mean "any four-digit number whose digits are all nonzero", then "no".

Mathematics all comes down to definitions....

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