How can I mathematically split up a 3 digit number?
up vote
10
down vote
favorite
For example, if I have 456, How can I split this and then let each column value be a separate number? The only way I can think of doing this would be to subtract '100' n times until that column is '0' and storing the number of subtractions, leaving '4' then repeating for the other columns. Is there a quicker way?
real-numbers
asked Nov 4 at 14:34
Ben Beaumont
615
add a comment |
up vote
10
down vote
favorite
For example, if I have 456, How can I split this and then let each column value be a separate number? The only way I can think of doing this would be to subtract '100' n times until that column is '0' and storing the number of subtractions, leaving '4' then repeating for the other columns. Is there a quicker way?
real-numbers
asked Nov 4 at 14:34
Ben Beaumont
615
1
Why not divide by $100?$
– saulspatz
Nov 4 at 14:36
3
What you describe is pretty much the normal straightforward way one would go about this, only its description (and implementation if you are going to program it) can be abbreviated using the notions of division with and without remainder and modulo, as described in the anwers. If the number happens to be in base 2 and you are doing it on a computer then there are also even faster shift operations.
– Nobody
Nov 4 at 20:27
add a comment |
up vote
10
down vote
favorite
up vote
10
down vote
favorite
For example, if I have 456, How can I split this and then let each column value be a separate number? The only way I can think of doing this would be to subtract '100' n times until that column is '0' and storing the number of subtractions, leaving '4' then repeating for the other columns. Is there a quicker way?
real-numbers
asked Nov 4 at 14:34
Ben Beaumont
615
For example, if I have 456, How can I split this and then let each column value be a separate number? The only way I can think of doing this would be to subtract '100' n times until that column is '0' and storing the number of subtractions, leaving '4' then repeating for the other columns. Is there a quicker way?
real-numbers
real-numbers
asked Nov 4 at 14:34
Ben Beaumont
615
asked Nov 4 at 14:34
Ben Beaumont
615
asked Nov 4 at 14:34
Ben Beaumont
615
asked Nov 4 at 14:34
Ben Beaumont
615
asked Nov 4 at 14:34
Ben Beaumont
615
615
1
Why not divide by $100?$
– saulspatz
Nov 4 at 14:36
3
What you describe is pretty much the normal straightforward way one would go about this, only its description (and implementation if you are going to program it) can be abbreviated using the notions of division with and without remainder and modulo, as described in the anwers. If the number happens to be in base 2 and you are doing it on a computer then there are also even faster shift operations.
– Nobody
Nov 4 at 20:27
add a comment |
1
Why not divide by $100?$
– saulspatz
Nov 4 at 14:36
3
What you describe is pretty much the normal straightforward way one would go about this, only its description (and implementation if you are going to program it) can be abbreviated using the notions of division with and without remainder and modulo, as described in the anwers. If the number happens to be in base 2 and you are doing it on a computer then there are also even faster shift operations.
– Nobody
Nov 4 at 20:27
1
1
Why not divide by $100?$
– saulspatz
Nov 4 at 14:36
Why not divide by $100?$
– saulspatz
Nov 4 at 14:36
3
3
What you describe is pretty much the normal straightforward way one would go about this, only its description (and implementation if you are going to program it) can be abbreviated using the notions of division with and without remainder and modulo, as described in the anwers. If the number happens to be in base 2 and you are doing it on a computer then there are also even faster shift operations.
– Nobody
Nov 4 at 20:27
What you describe is pretty much the normal straightforward way one would go about this, only its description (and implementation if you are going to program it) can be abbreviated using the notions of division with and without remainder and modulo, as described in the anwers. If the number happens to be in base 2 and you are doing it on a computer then there are also even faster shift operations.
– Nobody
Nov 4 at 20:27
add a comment |
2 Answers
2
active
oldest
votes
up vote
21
down vote
accepted
You can use the operation "modulo". It calculates the remainder after you have divided by a number.
- So 456 modulo 10 is 6, now you have the first digit.
- Then you can divide 456 with 10 without remainder, you get 45.
- Now 45 modulo 10 gives 5, now you have second digit.
- Then you can divide 45 with 10 without remainder, you get 4.
- Now 4 modulo 10 gives 4, now you have last digit.
edited Nov 5 at 0:07
NickA
1032
answered Nov 4 at 14:38
mathreadler
14.5k72160
7
Note that the 'ten' comes from decimal. This works in other number systems and you'll use the base-number of that number system instead of 'ten'.
– Jochem Kuijpers
Nov 5 at 1:28
1
"Divide without remainder" is also known as "divide and floor".
– Nayuki
Nov 5 at 6:53
2
and 'divide by the base' is also known as 'shift right'.
– amI
Nov 5 at 7:30
add a comment |
up vote
6
down vote
Divide $456$ with $100$ without remainder, you get $4$ - the first digit
Now $456 - 4cdot100 = 56$ - subtract $100$ times the first digit
Now divide $56$ with $10$ without remainder to get 5 - the second digit
Now do $56 - 5cdot10 = 6$ - last digit
You can use $mod{}$ to get them another way, from last (or first if you call it that way) to first digit
answered Nov 4 at 14:45
Aleksa
27512
1
The "last (or first if you call it that way)" ambiguity is resolved by using "most significant" and "least significant".
– Ben Voigt
Nov 5 at 4:52
add a comment |
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
21
down vote
accepted
You can use the operation "modulo". It calculates the remainder after you have divided by a number.
- So 456 modulo 10 is 6, now you have the first digit.
- Then you can divide 456 with 10 without remainder, you get 45.
- Now 45 modulo 10 gives 5, now you have second digit.
- Then you can divide 45 with 10 without remainder, you get 4.
- Now 4 modulo 10 gives 4, now you have last digit.
edited Nov 5 at 0:07
NickA
1032
answered Nov 4 at 14:38
mathreadler
14.5k72160
7
Note that the 'ten' comes from decimal. This works in other number systems and you'll use the base-number of that number system instead of 'ten'.
– Jochem Kuijpers
Nov 5 at 1:28
1
"Divide without remainder" is also known as "divide and floor".
– Nayuki
Nov 5 at 6:53
2
and 'divide by the base' is also known as 'shift right'.
– amI
Nov 5 at 7:30
add a comment |
up vote
21
down vote
accepted
You can use the operation "modulo". It calculates the remainder after you have divided by a number.
- So 456 modulo 10 is 6, now you have the first digit.
- Then you can divide 456 with 10 without remainder, you get 45.
- Now 45 modulo 10 gives 5, now you have second digit.
- Then you can divide 45 with 10 without remainder, you get 4.
- Now 4 modulo 10 gives 4, now you have last digit.
edited Nov 5 at 0:07
NickA
1032
answered Nov 4 at 14:38
mathreadler
14.5k72160
7
Note that the 'ten' comes from decimal. This works in other number systems and you'll use the base-number of that number system instead of 'ten'.
– Jochem Kuijpers
Nov 5 at 1:28
1
"Divide without remainder" is also known as "divide and floor".
– Nayuki
Nov 5 at 6:53
2
and 'divide by the base' is also known as 'shift right'.
– amI
Nov 5 at 7:30
add a comment |
up vote
21
down vote
accepted
up vote
21
down vote
accepted
You can use the operation "modulo". It calculates the remainder after you have divided by a number.
- So 456 modulo 10 is 6, now you have the first digit.
- Then you can divide 456 with 10 without remainder, you get 45.
- Now 45 modulo 10 gives 5, now you have second digit.
- Then you can divide 45 with 10 without remainder, you get 4.
- Now 4 modulo 10 gives 4, now you have last digit.
edited Nov 5 at 0:07
NickA
1032
answered Nov 4 at 14:38
mathreadler
14.5k72160
You can use the operation "modulo". It calculates the remainder after you have divided by a number.
- So 456 modulo 10 is 6, now you have the first digit.
- Then you can divide 456 with 10 without remainder, you get 45.
- Now 45 modulo 10 gives 5, now you have second digit.
- Then you can divide 45 with 10 without remainder, you get 4.
- Now 4 modulo 10 gives 4, now you have last digit.
edited Nov 5 at 0:07
NickA
1032
answered Nov 4 at 14:38
mathreadler
14.5k72160
edited Nov 5 at 0:07
NickA
1032
edited Nov 5 at 0:07
NickA
1032
edited Nov 5 at 0:07
NickA
1032
1032
answered Nov 4 at 14:38
mathreadler
14.5k72160
answered Nov 4 at 14:38
mathreadler
14.5k72160
answered Nov 4 at 14:38
mathreadler
14.5k72160
14.5k72160
7
Note that the 'ten' comes from decimal. This works in other number systems and you'll use the base-number of that number system instead of 'ten'.
– Jochem Kuijpers
Nov 5 at 1:28
1
"Divide without remainder" is also known as "divide and floor".
– Nayuki
Nov 5 at 6:53
2
and 'divide by the base' is also known as 'shift right'.
– amI
Nov 5 at 7:30
add a comment |
7
Note that the 'ten' comes from decimal. This works in other number systems and you'll use the base-number of that number system instead of 'ten'.
– Jochem Kuijpers
Nov 5 at 1:28
1
"Divide without remainder" is also known as "divide and floor".
– Nayuki
Nov 5 at 6:53
2
and 'divide by the base' is also known as 'shift right'.
– amI
Nov 5 at 7:30
7
7
Note that the 'ten' comes from decimal. This works in other number systems and you'll use the base-number of that number system instead of 'ten'.
– Jochem Kuijpers
Nov 5 at 1:28
Note that the 'ten' comes from decimal. This works in other number systems and you'll use the base-number of that number system instead of 'ten'.
– Jochem Kuijpers
Nov 5 at 1:28
1
1
"Divide without remainder" is also known as "divide and floor".
– Nayuki
Nov 5 at 6:53
"Divide without remainder" is also known as "divide and floor".
– Nayuki
Nov 5 at 6:53
2
2
and 'divide by the base' is also known as 'shift right'.
– amI
Nov 5 at 7:30
and 'divide by the base' is also known as 'shift right'.
– amI
Nov 5 at 7:30
add a comment |
up vote
6
down vote
Divide $456$ with $100$ without remainder, you get $4$ - the first digit
Now $456 - 4cdot100 = 56$ - subtract $100$ times the first digit
Now divide $56$ with $10$ without remainder to get 5 - the second digit
Now do $56 - 5cdot10 = 6$ - last digit
You can use $mod{}$ to get them another way, from last (or first if you call it that way) to first digit
answered Nov 4 at 14:45
Aleksa
27512
1
The "last (or first if you call it that way)" ambiguity is resolved by using "most significant" and "least significant".
– Ben Voigt
Nov 5 at 4:52
add a comment |
up vote
6
down vote
Divide $456$ with $100$ without remainder, you get $4$ - the first digit
Now $456 - 4cdot100 = 56$ - subtract $100$ times the first digit
Now divide $56$ with $10$ without remainder to get 5 - the second digit
Now do $56 - 5cdot10 = 6$ - last digit
You can use $mod{}$ to get them another way, from last (or first if you call it that way) to first digit
answered Nov 4 at 14:45
Aleksa
27512
1
The "last (or first if you call it that way)" ambiguity is resolved by using "most significant" and "least significant".
– Ben Voigt
Nov 5 at 4:52
add a comment |
up vote
6
down vote
up vote
6
down vote
Divide $456$ with $100$ without remainder, you get $4$ - the first digit
Now $456 - 4cdot100 = 56$ - subtract $100$ times the first digit
Now divide $56$ with $10$ without remainder to get 5 - the second digit
Now do $56 - 5cdot10 = 6$ - last digit
You can use $mod{}$ to get them another way, from last (or first if you call it that way) to first digit
answered Nov 4 at 14:45
Aleksa
27512
Divide $456$ with $100$ without remainder, you get $4$ - the first digit
Now $456 - 4cdot100 = 56$ - subtract $100$ times the first digit
Now divide $56$ with $10$ without remainder to get 5 - the second digit
Now do $56 - 5cdot10 = 6$ - last digit
You can use $mod{}$ to get them another way, from last (or first if you call it that way) to first digit
answered Nov 4 at 14:45
Aleksa
27512
answered Nov 4 at 14:45
Aleksa
27512
answered Nov 4 at 14:45
Aleksa
27512
answered Nov 4 at 14:45
Aleksa
27512
27512
1
The "last (or first if you call it that way)" ambiguity is resolved by using "most significant" and "least significant".
– Ben Voigt
Nov 5 at 4:52
add a comment |
1
The "last (or first if you call it that way)" ambiguity is resolved by using "most significant" and "least significant".
– Ben Voigt
Nov 5 at 4:52
1
1
The "last (or first if you call it that way)" ambiguity is resolved by using "most significant" and "least significant".
– Ben Voigt
Nov 5 at 4:52
The "last (or first if you call it that way)" ambiguity is resolved by using "most significant" and "least significant".
– Ben Voigt
Nov 5 at 4:52
add a comment |
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1
Why not divide by $100?$
– saulspatz
Nov 4 at 14:36
3
What you describe is pretty much the normal straightforward way one would go about this, only its description (and implementation if you are going to program it) can be abbreviated using the notions of division with and without remainder and modulo, as described in the anwers. If the number happens to be in base 2 and you are doing it on a computer then there are also even faster shift operations.
– Nobody
Nov 4 at 20:27